# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 - Matrics [Latest edition]

## Chapter 1: Matrics

MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics MCQ

#### 2 marks

MCQ | Q 1

The adjoint matrix of [(3, -3, 4),(2, -3, 4),(0, -1, 1)] is

• [(4, 8, 3),(2, 1,6),(0, 2, 1)]

• [(1, -1, 0),(-2, 3, -4),(-2, 3, -3)]

• [(11, 9, 3),(1, 2, 8),(6, 9, 1)]

• [(1, -2, 1),(-1, 3, 3),(-2, 3, -3)]

MCQ | Q 2

A = [(cos alpha, - sin alpha,  0),(sin alpha, cos alpha,  0),(0, 0, 1)], then A−1 is

• A

• − A

MCQ | Q 3

The solution (x, y, z) of the equation [(1, 0, 1),(-1, 1, 0),(0, -1, 1)] [(x),(y),(z)] = [(1),(1),(2)] is (x, y, z) =

• (1, 1, 1)

• (0, −1, 2)

• (−1, 2, 2)

• (−1, 0, 2)

MCQ | Q 4

If ω is a complex cube root of unity, then the matrix A = [(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)] is

• Singular matrix

• Non−symmetric matrix

• Skew−symmetric matrix

• Non−Singular matrix

MCQ | Q 5

If A = [(4, -1),(-1, "k")] such that A2 − 6A + 7I = 0, then K = ______

• 1

• 3

• 2

• 4

MCQ | Q 6

cos theta [(cos theta, sin theta),(-sin theta, cos  theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)] = ______

• [(0, 0),(0, 0)]

• [(0, 1),(1, 0)]

• [(1, 0),(0, 0)]

• [(1, 0),(0, 1)]

MCQ | Q 7

If A = [(0, 0, -1),(0, -1, 0),(-1, 0, 0)], then the only correct statement about the matrix A is ______

• A2 = I

• A is a zero matrix

• A−1 does not exit

• A = (−1) I, where I is a unit matrix

MCQ | Q 8

If A = [(cos alpha, sin alpha),(-sin alpha, cos 10 alpha)], then A10 = ______

• [(cos10  alpha, -sin10  alpha),(sin10  alpha, cos10  alpha)]

• [(cos10  alpha, sin10  alpha),(-sin10  alpha, cos10  alpha)]

• [(cos10  alpha, sin10  alpha),(-sin10  alpha, -cos10  alpha)]

• [(cos10  alpha, -sin10  alpha),(-sin10  alpha, -cos10  alpha)]

MCQ | Q 9

The element of second row and third column in the inverse of [(1, 2, 1),(2, 1, 0),(-1, 0, 1)] is ______

• −2

• −1

• 1

• 2

MCQ | Q 10

If A = [(4, 5),(2, 5)], then |(2A)−1| = ______

• 1/30

• 1/20

• 1/60

• 1/40

MCQ | Q 11

If [(x - y - z),(-y + z),(z)] = [(0),(5),(3)], then the value of x, y and z are respectively ______

• 0, −3, 3

• 1, −2, 3

• 5, 2, 2

• 11, 8, 3

MCQ | Q 12

The value of x, y, z for the following system of equations x + y + z = 6, x − y+ 2z = 5, 2x + y − z = 1 are ______

• x = 1, y = 2, z = 3

• x = 2, y = 1, z = 3

• x = −1, y = 2, z = 3

• x = y = z = 3

MCQ | Q 13

If A = [(3, 0, 0),(0, 3, 0),(0, 0, 3)], then |A| |adj A| = ______

• 33

• 39

• 36

• 327

MCQ | Q 14

System of equations x + y = 2, 2x + 2y = 3 has ______

• no solution

• only one solution

• many finite solutions.

• infinite solutions.

MCQ | Q 15

If A = [(1, -1, 1),(2, 1, -3),(1, 1, 1)], 10B = [(4, 2,2),(-5, 0, ∞),(1, -2, 3)] and B is the inverse of matrix A, then α = ______

• –2

• –1

• 2

• 5

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Very Short Answer

#### 1 Mark

Very Short Answer | Q 1

If A = [(1, 2, 3),(1, 1, 5),(2, 4, 7)], then find the value of a31A31 + a32A32 + a33A33

Very Short Answer | Q 2

For an invertible matrix A, if A . (adjA) = [(10, 0),(0, 10)], then find the value of |A|

Very Short Answer | Q 3

If the inverse of the matrix [(alpha, 14, -1),(2, 3, 1),(6, 2, 3)] does not exists then find the value of α

Very Short Answer | Q 4

If A = [(2, 2),(-3, 2)] and B = [(0, -1),(1, 0)], then find the matrix (B−1 A−1)−1

Very Short Answer | Q 5

A = [(cos theta, - sin theta),(-sin theta, -cos theta)] then find A−1

Very Short Answer | Q 6

If A = [("a", "b"),("c", "d")] then find the value of |A|−1

Very Short Answer | Q 7

If A = [(3, 1),(5, 2)], and AB = BA = I, then find the matrix B

Very Short Answer | Q 8

If A(α) = [(cos alpha, sin alpha),(-sin alpha, cos alpha)] then prove that A2(α) = A(2α)

Very Short Answer | Q 9

If A = [(1, 2),(3, -2),(-1, 0)] and B = [(1, 3, 2),(4, -1, 3)] then find the order of AB

Very Short Answer | Q 10

A + I = [(3, -2),(4, 1)] then find the value of (A + I)(A − I)

Very Short Answer | Q 11

If A = [(2, -1, 1),(-2, 3, -2),(-4, 4, -3)] the find A2

Very Short Answer | Q 12

If A = [(-2, 4),(-1, 2)] then find A2

Very Short Answer | Q 13

If A = [(0, 3, 3),(-3, 0, -4),(-3, 4, 0)] and B = [(x),(y),(z)], find the matrix B'(AB)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Short Answers I

#### 2 Marks

Short Answers I | Q 1

If f(x) = x2 − 2x − 3 then find f(A) when A = [(1, 2),(2, 1)]

Short Answers I | Q 2

If A = [(-1),(2),(3)], B = [(3, 1, -2)], find B'A'

Short Answers I | Q 3

If A is invertible matrix of order 3 and |A| = 5, then find |adj A|

Short Answers I | Q 4

If A = [(6, 5),(5, 6)] and B = [(11, 0),(0, 11)] then find A'B'

Short Answers I | Q 5

If A = [(2, 4),(1, 3)] and B = [(1, 1),(0, 1)] then find (A−1 B−1)

Short Answers I | Q 6

If A = [(2,0),(0, 1)] and B = [(1),(2)] then find the matrix 𝑋 such that A−1 X = B

Short Answers I | Q 7

Find the matrix X such that AX = I where A = [(6, 17),(1, 3)]

Short Answers I | Q 8

Find A–1 using adjoint method, where A = [(cos theta, sin theta),(-sin theta, cos theta)]

Short Answers I | Q 9.1

Find A−1 using column transformations:

A = [(5, 3),(3, -2)]

Short Answers I | Q 9.2

Find A−1 using column transformations:

A = [(2, -3),(-1, 2)]

Short Answers I | Q 10

Find the adjoint of matrix A = [(6, 5),(3, 4)]

Short Answers I | Q 11

Transform [(1, 2, 4),(3, -1, 5),(2, 4, 6)] into an upper triangular matrix by using suitable row transformations

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Short Answers II

#### 3 Marks

Short Answers II | Q 1

If A = [(0, 4, 3),(1, -3, -3),(-1, 4, 4)], then find A2 and hence find A−1

Short Answers II | Q 2

If A = [(0, 1),(2, 3),(1, -1)] and B = [(1, 2, 1),(2, 1, 0)], then find (AB)−1

Short Answers II | Q 3

If A = [(-4, -3, -3),(1, 0, 1),(4, 4, 3)], find adj (A)

Short Answers II | Q 4

Solve the following by inversion method 2x + y = 5, 3x + 5y = −3

Short Answers II | Q 5

If A = [(1, 2, -1),(3, -2, 5)], apply R1 ↔ R2 and then C1 → C1 + 2C3 on A

Short Answers II | Q 6

Three chairs and two tables cost ₹ 1850. Five chairs and three tables cost ₹2850. Find the cost of four chairs and one table by using matrices

Short Answers II | Q 7

If A = [(4,5),(2,1)], show that "A"^-1 = 1/6("A" - 5"I").

Short Answers II | Q 8

Find the adjoint of matrix A = [(2, 0, -1),(3, 1, 2),(-1, 1, 2)]

Short Answers II | Q 9

Find the matrix X such that [(1, 2, 3),(2, 3, 2),(1, 2, 2)] X = [(2, 2, -5),(-2, -1, 4),(1, 0, -1)]

Short Answers II | Q 10

Find the inverse of A = [(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]

Short Answers II | Q 11

Transform [(1, 2, 4),(3, -1, 5),(2, 4, 6)] into an upper triangular matrix by using suitable row transformations

Short Answers II | Q 12

If A = [(1, 0, 1),(0, 2, 3),(1, 2, 1)] and B = [(1, 2, 3),(1, 1, 5),(2, 4, 7)], then find the matrix X such that XA = B

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 1 Matrics Long Answers III

#### 4 Marks

Long Answers III | Q 1

Find the inverse of A = [(2, -3, 3),(2, 2, 3),(3, -2, 2)] by using elementary row transformations

Long Answers III | Q 2

If A = [(1, 0, 0),(3, 3, 0),(5, 2, -1)], find A−1 by the adjoint method

Long Answers III | Q 3

Solve the following equations by using inversion method.

x + y + z = −1, x − y + z = 2 and x + y − z = 3

Long Answers III | Q 5

Find the inverse of  A = [(1, 0, 1),(0, 2, 3),(1, 2, 1)] by elementary column transformations.

Long Answers III | Q 6

If A = [("x",0,0),(0,"y",0),(0,0,"z")] is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of [(2,0,0),(0,1,0),(0,0,-1)]

Long Answers III | Q 7

Find the inverse of A = [(costheta, -sintheta, 0),(sintheta, costheta, 0),(0, 0, 1)] by using elementary row transformations

Long Answers III | Q 8

If A = [(1,1),(1,2)], "B" = [(4,1),(3,1)] and C = [(24,7),(31,9)], then find the matrix X such that AXB = C

Long Answers III | Q 9

If A = [(1, -1, 2),(3, 0, -2),(1, 0, 3)], verify that A(adj A) = (adj A)A

Long Answers III | Q 10

If A = [(2, 3),(1, 2)], B = [(1, 0),(3, 1)], find AB and (AB)−1

Long Answers III | Q 11

Solve the following system of equations by using inversion method

x + y = 1, y + z = 5/3, z + x = 4/3

Long Answers III | Q 12

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is ₹ 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is ₹ 90. Whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is ₹ 70. Find the cost of each item per dozen by using matrices

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 1 - Matrics

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