ML Aggarwal solutions for Understanding ICSE Mathematics [English] Class 10 chapter 8 - Matrices [Latest edition]

`[(2, -1),(5, 1)]`

[2 3 – 7]

`[(3),(0),(-1)]`

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

`[(2 , 7, 8),(-1 , sqrt(2), 0)]`

`[(0, 0, 0),(0, 0, 0)]`

If a matrix has 4 elements, what are the possible order it can have?

If a matrix has 8 elements, what are the possible order it can have?

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 a_ij = i.j

Find the values of x and y if : `[(2x + y),(3x - 2y)] = [(5),(4)]`

Find the value of x if `[(3x + y, -y),(2y -  x, 3)] = [(1, 2),(-5, 3)]`

If `[(x + 3, 4),(y - 4, x + y)] = [(5, 4),(3, 9)]`,find values of x and y

Find the values of x, y and z if `[(x + 2, 6),(3, 5z)] = [(-5, y^2 + y),(3, 20)]`

Find the values of x, y, a and b if `[(x - 2, y),(a + 2b, 3a - b)]  = [(3, 1),(5, 1)]`

Find the values of a, b, c and d if `[(a + b, 3),(5 + c, ab)] = [(6, d),(-1, 8)]`

Find the values of x, y, a and b, if `[(3x + 4y, 2, x - 2y),(a + b, 2a - b, -1)] = [(2, 2, 4),(5, 5, 1)]`

Given that M = `[(2, 0),(1, 2)]` and N = `[(2, 0),(-1,2)]`, find M + 2N

If A = `[(2, 0),(-3, 1)]` and B = `[(0, 1),(-2, 3)]` find 2A – 3B

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

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 a matrix C such that C + B = `[(0, 0),(0, 0)]`

A = `[(1, 2),(-2, 3)]` and B = `[(-2, -1),(1, 2)], "C" [(0, 3),(2, -1)]`Find A + 2B – 3C

If A = `[(0, -1),(1, 2)]` and B = `[(1, 2),(-1, 1)]` Find the matrix X if : 3A + X = B

If A = `[(0, -1),(1, 2)]` and B = `[(1, 2),(-1, 1)]` Find the matrix X if : X – 3B = 2A

Solve the matrix equation `[(2, 1),(5, 0)] -3"X" = [(-7, 4),(2, 6)]`

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

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

Find X and Y If X + Y = `[(7, 0),(2, 5)]` and X – Y = `[(3, 0),(0, 3)]`

If `2[(3, 4),(5, x)] + [(1, y),(0, 1)] = [(7, 0),(10, 5)]` Find the values of x and y

If `2[(3, 4),(5, x)] + [(1, y),(0, 1)] = [(z, 0),(10, 5)]` Find the values of x and y

If `[(5, 2),(-1, y + 1)] -2 [(1, 2x - 1),(3, -2)] = [(3, -8),(-7, 2)]` Find the values of x and y

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

If A = `[(2, a),(-3, 5)] and "B" = [(-2, 3),(7, b)], "C" = [(c, 9),(-1, -11)]` and 5A + 2B = C, find the values of a,b,c

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

If A = `[(2, 5),(1, 3)] "B" = [(1, -1),(-3, 2)]` , find AB and BA, Is AB = BA ?

If P = `[(4, 6),(2 ,- 8)], "Q" = [(2, -3),(-1, 1)]` Find 2PQ

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

If A = `[(3, 7),(2, 4)], "B" = [(0, 2),(5, 3)] and "C" = [(1, -5),(-4, 6)]` Find AB – 5C

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

Given martices A = `[(2, 1),(4, 2)] and "B" = [(3, 4),(-1, -2)], "C" = [(-3, 1),(0, -2)]` Find the products of (i) ABC (ii) ACB and state whether they are equal.

Evaluate : `[(4sin30°, 2cos60°),(sin90°, 2cos0°)] [(4, 5),(5, 4)]`

If A = `[(-1, 3),(2, 4)], "B" = [(2, -3),(-4, -6)]` find the matrix AB + BA

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

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

If A = `[(1 , -2),(2, -1)] and "B" = [(3, 2),(-2, 1)]` Find 2B – A² 

If A = `[(1, 2),(3, 4)] and "B" = [(2, 1),(4, 2)], "C" = [(5, 1),(7, 4)]`, compute A(B + C)

If A = `[(1, 2),(3, 4)] and "B" = [(2, 1),(4, 2)], "C" = [(5, 1),(7, 4)]`, compute (B + C)A

If A = `[(1, 2),(2, 3)] and "B" = [(2, 1),(3, 2)], "C" = [(1, 3),(3, 1)]` find the matrix C(B – A)

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

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

If A = `[(1, 0),(0, -1)]`, find A2 and A3.Also state that which of these is equal to A

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

Show that `[(1, 2),(2, 1)]` is a solution of the matrix equation X² – 2X – 3I = 0,Where I is the unit matrix of order 2

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

If A = `[(1, 1),(x, x)]`,find the value of x, so that A² – 0

If `[(1, 3),(0, 0)] [(2),(-1)] = [(x),(0)]` Find the value of x

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

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

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

If `[(1, 2),(3, 3)] [(x, 0),(0, y)] = [(x, 0),(9, 0)]`find the values of x and y

If `[(3, 4),(5, 5)] = [(a, b),(c, d)] [(1, 0),(0, 1)]`write down the values of a,b,c and d

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

If A = `[(2, x),(0, 1)] and "B" = [(4, 36),(0, 1)]`,find the value of x, given that A² – B

If A = `[(3, x),(0, 1)] and "B" = [(9, 16),(0, -y)]`find x and y when A² = B

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

If `[(a, 1),(1, 0)] [(4, 3),(-3, 2)] = [(b, 11),(4, c)]` find a,b and c

If A = `[(1, 4),(0, -1)], "B" = [(2, x),(0, -1/2)]`find the value of x if AB = BA

If A = `[(2, 3),(1, 2)]` find x and y so that A² – xA + yI

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

Let `"M" xx [(1, 1),(0, 2)]` = [1 2] where M is a matrix.

1. State the order of matrix M
2. Find the matrix M

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.

Solve the matrix equation : `[(4),(1)],"X" = [(-4, 8),(-1, 2)]`

If A = `[(2, -1),(-4, 5)] and "B" = [(-3),(2)]` find the matrix C such that AC = B

If A = `[(2 , -1),(-4, 5)]` and B = [0 -3] find the matrix C such that CA = B

If A = `[(3, -4),(-1, 2)]`, find matrix B such that BA = I,where I is unity matrix of order 2

If B = `[(-4, 2),(5, -1)] and "C" = [(17, -1),(47, -13)]` find the matrix A such that AB = C

Choose the correct answer from the given four options :

If A = [a_ij]_2×2 where a_ij = i + j, then A is equal to

Choose the correct answer from the given four options :

If `[(x + 3, 4),(y - 4, x + y)] = [(5, 4),(3, 9)]` then the values of x and y are

Choose the correct answer from the given four options :

If `[(x + 2y, -y),(3x, 7)] = [(-4, 3),(6, 4)]` then the values of x and y are

Choose the correct answer from the given four options :

If `[(x - 2y, 5),(3, y)] = [(6, 5),(3, -2)]` then the value of x is

Choose the correct answer from the given four options :

If `[(x + 2y, 3y),(4x, 2)] = [(0, -3),(8, 2)]` then the value of x – y is

Choose the correct answer from the given four options :

If `x[(2),(3)] + y[(-1),(0)] = [(10),(6)]` then the values of x and y are

Choose the correct answer from the given four options :

If B = `[(1, 5),(0, 3)]` and A – 2B = `[(0, 4),(-7, 5)]` then the matrix A is equal to

Choose the correct answer from the given four options :

If A + B = `[(1, 0),(1, 1)]` and A – 2B = `[(-1, 1),(0, -1)]` then A is equal to

Choose the correct answer from the given four options :

A = `[(1, 0),(0, 1)]` then A² =

Choose the correct answer from the given four options :

If A = `[(0, 1),(1, 0)]`, then A² =

Choose the correct answer from the given four options :

If A = `[(0, 0),(1, 0)]`, then A² = 

Choose the correct answer from the given four options :

If A = `[(1, 0),(1, 1)]`, then A² =

Choose the correct answer from the given four options :

If A = `[(3, 1),(-1, 2)]`, then A² = 

Choose the correct answer from the given four options :

If A = `[(2, -2),(-2, 2)]`, then A² = pA, then the value of p is

Find the values of a and below `[(a + 3, b^2 + 2),(0, -6)] = [(2a + 1, 3b),(0, b^2 - 5b)]`

Find a, b, c and d if `3[(a, b),(c, d)] = [(4, a + b),(c + d, 3)] + [(a, 6),(-1, 2d)]`

Find X if Y = `[(3, 2),(1, 4)]` and 2X + Y = `[(1, 0),(-3, 2)]`

Determine the matrices A and B when A + 2B = `[(1, 2),(6, -3)] and 2"A" - "B" = [(2, -1),(2, -1)]`

Find the matrix B if A = `[(4, 1),(2, 3)]` and A² = A + 2B

If A = `[(1, 2),(-3, 4)], "B" = [(0, 1),(-2, 5)] and "C" = [(-2, 0),(-1, 1)]` find A(4B – 3C)

If A = `[(1, 4),(1, 0)], "B" = [(2, 1),(3, -1)] and "C" = [(2, 3),(0, 5)]` compute (AB)C = (CB)A ?

If A = `[(3, 2),(0, 5)] and "B" = [(1, 0),(1, 2)]` find the each of the following and state it they are equal: (A + B)(A – B)

If A = `[(3, 2),(0, 5)] and "B" = [(1, 0),(1, 2)]` find the each of the following and state it they are equal: A² – B²  

If A = `[(3, -5),(-4, 2)]` find A² – 5A – 14I
Where I is unit matrix of order 2 x 2

If A = `[(3, 3),(p, q)]` and A² = 0 find p and q

If A = `[(3/5, 2/5),(x, y)]` and A² = I, find x,y

If `[(-1, 0),(0, 1)] [(a, b),(c, d)] = [(1, 0),(0, -1)]` find a,b,c and d

Find a and b if `[(a - b, b - 4),(b + 4, a - 2)] [(2, 0),(0, 2)] = [(2, -2),(14, 0)]`

If A = `[(sec60°, cos90°),(-3tan45°, sin90°)] and "B" = [(0, cos45°),(-2, 3sin90°)]` Find : 2A – 3B

If A = `[(sec60°, cos90°),(-3tan45°, sin90°)] and "B" = [(0, cos45°),(-2, 3sin90°)]` Find : A² 

If A = `[(sec60°, cos90°),(-3tan45°, sin90°)] and "B" = [(0, cos45°),(-2, 3sin90°)]` Find : BA