#### Chapters

Chapter 2 - Banking (Recurring Deposit Account)

Chapter 3 - Shares and Dividend

Chapter 4 - Linear Inequations (In one variable)

Chapter 5 - Quadratic Equations

Chapter 6 - Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7 - Ratio and Proportion (Including Properties and Uses)

Chapter 8 - Remainder and Factor Theorems

Chapter 9 - Matrices

Chapter 10 - Arithmetic Progression

Chapter 11 - Geometric Progression

Chapter 12 - Reflection

Chapter 13 - Section and Mid-Point Formula

Chapter 14 - Equation of a Line

Chapter 15 - Similarity (With Applications to Maps and Models)

Chapter 16 - Loci (Locus and Its Constructions)

Chapter 17 - Circles

Chapter 18 - Tangents and Intersecting Chords

Chapter 19 - Constructions (Circles)

Chapter 20 - Cylinder, Cone and Sphere

Chapter 21 - Trigonometrical Identities

Chapter 22 - Height and Distances

Chapter 23 - Graphical Representation

Chapter 24 - Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25 - Probability

## Chapter 9 - Matrices

#### Page 0

State, whether the following statements are true or false. If false, give a reason.

If A and B are two matrices of orders 3 × 2 and 2 × 3 respectively; then their sum A + B is possible.

State, whether the following statements are true or false. If false, give a reason.

The matrices A_{2 × 3} and B_{2 × 3} are conformable for subtraction.

State, whether the following statement is true or false. If false, give a reason.

Transpose of a 2 × 1 matrix is a 2 × 1 matrix.

State, whether the following statements are true or false. If false, give a reason.

Transpose of a square matrix is a square matrix.

State, whether the following statements are true or false. If false, give a reason.

A column matrix has many columns and one row.

Given `[(x, y + 2),(3, z - 1)] = [(3,1),(3,2)]`, Find x, y, z

Solve for a, b and c if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`

Solve for a, b and c if `[(a, a- b),(b + c, 0)] = [(3, -1),(2,0)]`

If A = [8 -3] and B = [4 -5]; find A + B

If A = [8 -3] and B = [4 -5]; find B - A

If `A = [2/5]`,` B = [1/4]` and `C = [6/-2]` Find B + C

If A = `[2/5], B = [1/ 4] and c = [6/-2] `Find A - C

if `A = [(2),(5)], B = [(1),(4)] and C = [(6),(-2)]` Find A + B - C

If A = `[2/5], B = [1/4] and C =[6/-2], `find :

A – B +C

Wherever possible write of the following as a single matrix

`[(1, 2),(3, 4)] +[(-1,-2), (1,-7)]`

Wherever possible write of the following as a single matrix

`[(2,3,4),(5,6,7)] - [(0,2,3),(6,-1,0)]`

Wherever possible write of the following as a single matrix

`[(0,1,2),(4,6,7)] + [(3,4),(6,8)]`

Find x and y from the given equations:

`[(5,2),(-1, y - 1)] - [(1, x -1),(2, -3)] = [(4,7),(-3,2)]`

Find x and y from the given equations:

[-8 x] + [y -2] = [-3 2]

Given M = `[(5, -3),(-2, 4)]` Find its transpose matrix `M^t`. If possible find `M + M^t`

Given `M = [(5, -3),(-2, 4)]` find its transpose matrix `M^t` if possible find `M^t - M`

Write the additive inverse of matrices A, B and C Where A = [6, -5]; B = `[(-2, 0),(4, -1)] and C = [(-7), (4)]`

Given A = [2 -3], B = [0 2] and C = [-1 4]; Find the matrix X in the following:

X + B = C - A

Given A = [2 -3], B = [0 2] and C = [-1 4]; Find the matrx X in the following

A - X = B + C

Given `A = [(-1, 0),(2, -4)] and B = [(3, -3),(-2, 0)]` Find the matrix X in the following

A + X = B

Given A` = [(-1, 0),(2,0)]` and B = `[(3, -3),(-2, 0)]` find the matrix X in of the following

A- X = B

Given `A = [(-1, 0),(2, -4)]` and `B = [(3, -3),(-2, 0)]` Find the matrix X in following

X - B = A

#### Page 0

Evaluate 3[5 -2]

Evaluate `7[(-1, 2),(0, 1)]`

Evaluate : `2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`

Evaluate `6[(3), (-2)] -2[(-8), (1)]`

Find x and y if 3[4 x] + 2[y -3] = [10 0]

Find x and y if `x[(-1), (2)] - 4[(-2), (y)] = [(7),(-8)]`

Given `A = 2[(2, 1),(3, 0)],-3[(1, 1),(5, 2)] + [(-3, -1),(0,0)]` Find 2A - 3B + C

Given A = `2[(2,1),(3,0)]-3[(1,1),(5,2)]+[(-3, -1),(0,0)]`: find A + 2C – B

If `[(4, -2),(4, 0)] + 3A = [(-2,-2),(1, -3)]` Find A

Given `A = [(1, 4),(2, 3)] and B = |(-4-1),(-3 -2)|`

Find the matrix 2A + B

Given `A = [(1 4),(2 3)] and B = [(-4 -1),(-3 -2)]` Find the matrix C such that C + B = `[(0, 0),(0,0)]`

If `2[(3, x),(0, 1)] + 3[(1, 3),(y, 2)] = [(z, -7),(15, 8)]` Find the values of x, y and z.

Given `A = [(-3, 6),(0, -9)]` and `A^t` its transpose matrix. Find `2A + 3A^t`

Given `A = [(-3, 6),(0, -9)]` and `A^t` is its transpose matrix Find `2A^t - 3A`

Given `A = [(-3, 6),(0, -9)]` and `A^t` is its transpose matrix. Find `1/2 A - 1/3 A^t`

Given `A = [(-3, 6),(0, -9)]` and `A^t` is its transpose matrix Find `A^t - 1/3 A`

Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1),(1, 1)]`

Solve for matrix X:

X + 2A = B

Given `A = [(1,1),(-2, 0)]` and `B = [(2, -1), (1, 1)]` Solve for matrix X

3X + B + 2A = O

Given A = `[(1,1),(-2, 0)]` and `B = [(2, -1),(1, 1)]` Solve for matrix X:

3A - 2X = X - 2B

If `M = [(0), (1)]` and `N = [(1),(0)]` show that `3M + 5N = [5/3]`

If I is the unit matrix of order 2 x 2 Find the matrix M such that `M - 2I = 3[(-1, 0),(4, 1)]`

If I is the unit matrix of order 2 x 2. Find the matrix M such that

`5M + 3I = 4[(2, -5),(0, -3)]`

If `[(1, 4),(-2, 3)] + 2M = 3[(3, 2),(0, -3)]`, find the matrix M

#### Page 0

Evaluate if possible `[(3 ,2)][(2),(0)]`

Evaluate if possible `[(1, -2)][(-2, 3),(-1, 4)]`

Evaluate if possible `[(6, 4),(3, -1)][(-1),(3)]`

Evaluate if possible `[(6, 4),(3, 1)][-1, 3]`

If `A = [(0, 2),(5, -2)]`, `B= [(1, -1),(3, 2)]` and I is a unit matrix of order 2 x 2 find AB

If `A = [(0, 2),(5, -2)], B = [(1, -1),(3, 2)]` and I is a unit matrix of order 2 x 2 findb BA

If `A = [(0, 2),(5, -2)]`, B =` [(1, -1),(3, 2)]` and I is a unit matrix of order 2 x 2. Find AI

If `A= [(0, 2),(5, -2)], B = [(1, -1),(3, 2)]` and I is unit matrix of order 2 x 2 Find IB

If `A = [(0, 2),(5, -2)], B = [(1, -1),(3, 2)]` and I is a unit matrix of order 2 x 2 find `A^2`

If `A = [(0, 2),(5, -2)], B = [(1, -1),(3, 2)]` and I is unit matrix of order 2 x 2 find `B^2A`

If M = `[(2,1),(1,-2)] `; find M^{2}, M^{3} and M^{5}.

Find x and y if `[(4, 3x),(x, -2)][(5), (1)] = [(y),(8)]`

Find x and y if `[(x, 0),(-3, 1)][(1,1),(0, y)] = [(2,2),(-3, -2)]`

If `A = [(1, 3),(2, 4)], B = [(1, 2),(4, 3)] and C = [(4, 3),(1, 2)]` find

1) (AB)C

2) A(BC)

Is A(BC) = (AB)C?

Given `A = [(0, 4, 6),(3, 0, -1)]` and B = `[(0, 1),(-1, 2),(-5, -6)]` find if possible AB

Given `A = [(0, 4, 6),(3, 0, -1)]` and `B = [(0, 1),(-1, 2),(-5, -6)]` find if possible BA

Given `A = [(0, 4, 6),(3, 0, 1)][(0, 1),(-1, 2),(-5, -6)]` Find if possible `A^2`

`If A = [(1, -2 ,1), (2,1,3)] and B= [(2,1),(3,2),(1,1)]`;

Write down the product matrix AB.

If A =` [(1,-2 ,1),(2,1,3)]and B=[(2,1),(3,2),(1,1)]`

would it be possible to form the product matrix BA? If so, compute BA; if not give a reason

why it is not possible.

If `M =[(1, 2),(2, 1)]` and I is a unit matrix of the same order as that of M Show that `M^2 = 2M + 3I`

If `A = [(a, 0),(0, 2)]`, B = `[(0, -b),(1, 0)], M = [(1, -1),(1, 1)]` and `BA = M^2` find the values of a and b.

Given `A = [(4, 1),(2,3)]` and `B = [(1, 0),(-2, 1)]` Find A - B

Given `A = [(4, 1), (2, 3)]` and `B = [(1, 0),(-2, 1)]` Find `A^2`

Given `A = [(4, 1),(2, 3)]` and `B = [(1, 0),(-2, 1)]` Find AB

Given `A = [(4, 1),(2, 3)]` and `B = [(1, 0),(-2, 1)]` Find `A^2 - AB + 2B`

If `A = [(1, 4), (1, -3)]` and `B = [(1, 2),(-1, -1)]` Find `(A + B)^2`

If `A = [(1, 4),(1, -3)]` and `B = [(1, 2),(-1, -1)]` Find `A^2 + B^2`

If A= [(1, 4), (1, -3)] and `B = [(1, 2),(-1, -1)]` Find : Is `(A + B)^2 = A^2 + B^2?`

Find the matrix A, If B =`[(2,1),(0,1)] and B^2 = B+1/2A`

If `A = [(-1, 1),(a, b)]` and `A^2 = I`; Find a and b

If `A = [(2, 1),(0, 0)] , B = [(2, 3),(4, 1)] and C = [(1, 4),(0, 2)]` then show that A(B + C) = AB + AC

If` A = [(2, 1),(0,0)], B = [(2, 3),(4, 1)] and C = [(1, 4),(0, 2)]` then show that (B - A)C = BC - AC

If `A = [(1, 4),(2, 1)], B = [(-3, 2),(4, 0)]] and C = [(1, 0),(0, 2)]` Simplify `A^2 + BC`

Solve for x and y: `[(2, 5),(5, 2)][(x),(y)] = [(-7),(14)]`

Solve for x and y :

`[(3,-1),(2,-1)][(-2),(4)]=[(x),(y)]`

Solve for x and y :

`[x+y x-4] [(-1,-2),(2,2)] = [-7 -11]`

In the given case below find

a) The order of matrix M.

b) The matrix M

`M xx [(1,1),(0, 2)] = [1, 2]`

In the given case below, Find :

a) The order of matrix M

b) The matrix M

`[(1, 4),(2, 1)] xx M = [(13), (5)]`

If `A = [(2, x),(0, 1)] and B = [(4, 36),(0, 1)]`. Find the vlaue of x given that `A^2 = B`

Find the positive integers p and q such that :

`[p q][p/q]= [25]`

If A and B are any two 2 x 2 matrices such that AB = BA = B and B is not a zero matrix, what can you say about the matrix A?

Given `A = [(3, 0),(0, 4)]`, `B = [(a, b),(0, c)]` and that AB = A + B. Find the values of a, b and c

If `P = [(1, 2),(2, -1)] and Q = [(1, 0),(2, 1)]` then compute:

1) `P^2 - Q^2`

2) (P + Q)(P - Q)

`Is (P + Q)(P - Q) = P^2 - Q^2` true for matrix algebra?

Given the matrices `A = [(2, 1),(4, 2)], B = [(3, 4),(-1, -2)] and C = [(-3, 1),(0, -2)]` Find

1) ABC

2) ACB

State whether ABC = ACB.

If `A = [(1, 2),(3, 4)]`, `B = [(6, 1), (1, 1)]` and `C= [(-2, -3),(0, 1)]` Find the following and state of they are equal CA + B

If `A = [(1, 2),(3, 4)], B = [(6, 1), (1, 1)] and C = [(-2, -3),(0, 1)]` find of the following and state if they are equal A + CB

if `A = [(2, 1),(1, 3)]` and `B = [(3),(-11)]` Fidn the matrix X such that AX = B

If `A =[(4, 2),(1,1)]` Find (A - 2I)(A - 3I)

If `A = [(2, 1, -1),(0, 1, -2)]` Find `A^t. A` Where `A^t.A` is the transpose of matrix A

If `A = [(2,1,-1),(0, 1,-2)]` find `A.A^t` where `A^t` is the transpose of matrix A

if M = `[(4,1),(-1,2)]` show that `6m - m^2 = 9I` where I is 2 x 2 unit matrix.

If `P = [(2,6),(3,9)]` and `Q = [(3,x),(y, 2)]` find x and y such that PQ = null matrix

Evaluate without using tables:

`[(2 cos 60^@ - 2 sin 30^@),(-tan 45^@ , cos 0^@)][(cot 45^@,cosec 30^@),(sec 60^@,sin 90^@)]`

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2

A + B = B + A

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

A – B = B – A

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

(B. C). A = B. (C. A)

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

(A + B). C = A. C + B. C

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

A. (B - C) = A. B - A. C

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

(A – B). C = A. C – B. C

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

A² – B² = (A + B) (A – B)

State, with reason, whether the following are true or false. A, B and C are matrices of order 2 x 2.

(A – B)² = A² – 2A. B + B²

#### Page 0

Find x and y if `[(3,-2),(-1,4)][(2x),(1)] + 2[(-4),(5)] = 4[(2),(y)]`

Find x and y if `[3x 8][(1,4),(3,7)] - 3[(2,-7)] = 5[(3, 2y)]`

if `[x,y][(x),(y)]` = [25] and `[-x, y][(2x),(y)] = [-2]` find x and y if `x, y ε W` (whole numbers)

If `[x, y][(x),(y)] = [25]` and `[(-x, y)][(2x),(y)] = [-2]` find x and y if `x, y ε Z` (integer)

Given `[(2, 1),(-3, 4)] X = [(7), (6)]` write the order of matrix x

Given `[(2, 1),(-3, 4)] x = [(7),(6)]` Write the matrix x

Evaluate `[(cos 45°, sin 30°),(sqrt2 cos 0°, sin 0°)][(sin 45°, cos 90°), (sin 90°, cot 45°)]`

If `A = [(0, -1),(4, -3)]`, B = `[(-5),(6)]` and 3A x M = 2B; Find matrix M

If `[(a, 3),(4, 1)] + [(2, b),(1, -2)] - [(1,1),(-2, c)] = [(5, 0),(7, 3)]`, Find the values of a, b and c

If `A = [(1, 2),(2,1)]` and `B = [(2, 1),(1, 2)]` Find A(BA)

If `A = [(1, 2),(2, 1)]` and `B= [(2,1),(1, 2)]` Find (AB).B

Find x and y if `[(x, 3x),(y, 4y)][(2), (1)] = [(5),(12)]`

If matrix `X = [(-3, 4),(2, -3)][(2),(-2)]` and 2X - 3Y = `[(10),(-8)]`; Find the matrix X and Y

Given `A = [(2, -1),(2, 0)] B = [(-3, 2),(4, 0)]` and `C = [(1, 0),(0, 2)]` Find the matrix X such that A + X = 2B = C

Find the value of x, given that `A^2 = B`

`A = [(2, 12),(0, 1)] and B = [(4, x),(0, 1)]`

If `A = [(2, 5),(1, 3)]`, `B = [(4, -2),(-1, 3)]` and I is Identity matrix of same order and `A^t` is the transpose of matrix A find `A^t.B + BI`

Given A = `[(2,-6),(2,0)], B = [(-3,2),(4,0)], C = [(4,0),(0,2)]`

Find the matrix X such that A + 2X = 2B + C.

Let `A = [(4, -2),(6, -3)], B = [(0, 2),(1, -1)] and C =[(-2, 3),(1, -1)]` Find `A^2 + A +BC`

Let `A = [(1, 0),(2, 1)], B = [(2, 3),(-1, 0)]`. Find `A^2 + AB + B^2`

If `A = [(3, a),(-4, 8)], B = [(c, 4),(-3, 0)], C = [(-1, 4),(3, b)]` and 3A - 2C = 6B, find the values of a, b , c.

Given `A = [(p, 0),(0, 2)], B = [(0, -q),(1, 0)] C = [(2, -2),(2, 2)]` and `BA = C^2` Find the values of p and q

Given `A = [(3,-2),(-1,4)] B = [(6),(1)], C = [(-4),(5)] and D = [(2),(2)]` Find AB + 2C - 4D

Evaluate:

`[(4sin 30^@, 2cos 60^@),(sin 90^@, 2 cos 0^@)][(4,5),(5,4)]`

if A = `[(3,1),(-1,2)]` and `I = [(1,0),(0,1)]`, find `A^2 - 5A + 7I`