R.S. Aggarwal solutions for Mathematics [English] Class 10 ICSE chapter 9 - Matrices [Latest edition]

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

Given `[(2, 1),(-3, 4)] "X" = [(7),(6)]`.
the matrix X.

If A = `[(3, 5),(4,- 2)]` and B = `[(2),(4)]`, is the product AB possible ? Given a reason. If yes, find AB.

Find the value of p and q if:
`[(2p + 1 , q^2 - 2),(6 , 0)] = [(p + 3, 3q - 4),(5q - q^2, 0)]`.

Given A = `[(p , 0),(0, 2)], "B" = [(0 , -q), (1, 0)], "C" = [(2, -2),(2, 2)]` and BA = C².
Find the values of p and q.

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

If A = `[(2, 4),(3, 2)]` and B = `[(1, 3),(-2, 5)]`
find AB,

If A = `[(2, 4),(3, 2)]` and B = `[(1, 3),(-2, 5)]`
find BA.

Find x and y, if
`[(-3, 2),(0, -5)] [(x),(2)] = [(-5), (y)]`

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

Find X and Y, if
`[(2x, x),(y , 3y)][(3),(2)] = [(16),(9)]`

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

Find the value of x given that A²  = B
A = `[(2, 12),(0 , 1)]` B = `[(4, x),(0, 1)]`

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

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

Find x and y if:
`((-3, 2),(0 , 5)) ((x),(y)) = ((-5),(y))`

Construct a 2 x 2 matrix whose elements a_ij are given by
a_ij = 2i - j

Construct a 2 x 2 matrix whose elements a_ij are given by `((i + 2j)^2)/(2)`.

Given
`"A" = [(2 , -6),(2, 0)] "B" = [(-3, 2),(4, 0)], "C" = [(4, 0),(0, 2)]`
Find the martix X such that A + 2X = 2B + C.

Find matrices X and Y, if
X + Y = `[(5, 2),(0, 9)]` and X - Y = `[(3 , 6),(0, -1)]`

If A = `[(3 , 1),(-1 , 2)]` and I = `[(1 , 0),(0, 1)]`
find A² - 5A + 7 I.

If A = `[(9 , 1),(7 , 8)]` , B = `[(1 , 5),(7 , 12)]`
find matrix C such that 5A + 5B + 2C is a null matrix.

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

If A = `[(1 , 0),(-1 ,7)]` and I = `[(1 , 0),(0 ,1)]`, then find k so that A² = 8A + kI.

A = `[(3 , 1),(-1 , 2)]`, show that A² - 5A + 7 I₂ = 0.

If A = `[(3 , 1),(-1 , 2)]` and B =`[(7),(0)]`, find matrix C if AC = B.

If X = `[(4 , 1),(-1 , 2)]`, show that 6X - X² = 9I, where I is unit matrix.

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

Given A = `[(1, 1),(8, 3)]` evaluate A² − 4A.

Let A = `[(2, 1),(0, -2)]`, B = `[(4, 1),(-3, -2)]` and C = `[(-3, 2),(-1, 4)]`. Find A² + AC – 5B.

Find the 2 x 2 matrix X which satisfies the equation.
`[(3, 7),(2, 4)][(0 , 2),(5 , 3)] + 2"X" = [(1 , -5),(-4 , 6)]`

If A = `[(9 , 1),(5 , 3)]` and B = `[(1 , 5),(7 , -11)]`, find matrix X such that 3A + 5B - 2X = 0.

Let `"A" = [(4 , -2),(6 , -3)], "B" = [(0 , 2),(1 , -1)] and "C" = [(-2 , 3),(1 , -1)]`. Find A² - A + BC

Let A = `[(1, 0),(2, 1)]`, B = `[(2, 3),(-1, 0)]`, Find A² + AB + B².

If `"A" = [(a , b),(c , d)] and "I" = [(1 , 0),(0 , 1)]` show that A² - (a + d) A = (bc - ad) I.

If `"A" = [(1 , 2),(-2 , 3)], "B" = [(2 , 1),(2 , 3)] "C" = [(-3 , 1),(2 , 0)]` verify that
(AB)C = A(BC),

If `"A" = [(1 , 2),(-2 , 3)], "B" = [(2 , 1),(2 , 3)] "C" = [(-3 , 1),(2 , 0)]` verify that
A(B + C) = AB + AC.

If `"A" = [(3 , 1),(2 , 1)] and "B" = [(1 , -2),(5 , 3)]`, then show that (A - B)² ≠ A2 - 2AB + B².