M l aggarwal understanding icse mathematics class 10 Solutions for Chapter 7 matrices

Given that

M=\left[\begin{array}{ll} 2 & 0 \\ 1 & 2 \end{array}\right] and \mathrm{N}=\left[\begin{array}{cc} 2 & 0 \\ -1 & 2 \end{array}\right], \text { find } M+2 N

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

(ii) If a matrix has 4 elements, what are the possible orders it can have?

Construct a 2 × 2 matrix whose elements aij are given by

(i) aij = 2i – j

(ii) aij =i.j

Find the values of x and y if:

\left[\begin{array}{l} 2 x+y \\ 3 x-2 y \end{array}\right]=\left[\begin{array}{l} 5 \\ 4 \end{array}\right]

Find the value of x if

\left[\begin{array}{rr} 3 x+y & -y \\ 2 y-x & 3 \end{array}\right]=\left[\begin{array}{cc} 1 & 2 \\ -5 & 3 \end{array}\right]

If

\left[\begin{array}{cc} x+3 & 4 \\ y-4 & x+y \end{array}\right]=\left[\begin{array}{ll} 5 & 4 \\ 3 & 9 \end{array}\right]

Find the values of x and y.

Find the values of x, y and z if

\left[\begin{array}{lr} x+2 & 6 \\ 3 & 5 z \end{array}\right]=\left[\begin{array}{cc} -5 & y^{2}+y \\ 3 & -20 \end{array}\right]

Find the values of x, y, a, and b if

\left[\begin{array}{cc} x-2 & y \\ a+2 b & 3 a-b \end{array}\right]=\left[\begin{array}{ll} 3 & 1 \\ 5 & 1 \end{array}\right]

Find the values of a, b, c and d if

\left[\begin{array}{ll} a+b & 3 \\ 5+c & a b \end{array}\right]=\left[\begin{array}{cc} 6 & d \\ -1 & 8 \end{array}\right]

Find the values of x, y, a, and b, if

\left[\begin{array}{c} 3 x+4 y-x-2 y \\ a+b 2 a-b-1 \end{array}\right]=\left[\begin{array}{ccc} 2 & 2 & 4 \\ 5 & -5 & -1 \end{array}\right]

\begin{array}{l} \text { If } A=\left[\begin{array}{cc} 2 & 0 \\ -3 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{cc} 0 & 1 \\ -2 & 3 \end{array}\right] \end{array}

\text { find } 2 A-3 B

\text { If } A=\left[\begin{array}{ll} 1 & 4 \\ 2 & 3 \end{array}\right] \text { and } B=\left[\begin{array}{ll} 1 & 2 \\ 3 & 1 \end{array}\right] \text { Compute } 3 \mathrm{A}+4 \mathrm{B}

\text { Given } A=\left[\begin{array}{ll} 1 & 4 \\ 2 & 3 \end{array}\right] \text { and } B=\left[\begin{array}{ll} -4 & -1 \\ -3 & -2 \end{array}\right]

\text { (i) find the matrix } 2 A+B

\text { (ii) find a matrix } C \text { such that } C+B=\left[\begin{array}{ll} 0 & 0 \\ 0 & 0 \end{array}\right]

A=\left[\begin{array}{cc} 1 & 2 \\ -2 & 3 \end{array}\right] \text { and } B=\left[\begin{array}{cc} -2 & -1 \\ 1 & 2 \end{array}\right], C=\left[\begin{array}{cc} 0 & 3 \\ 2 & -1 \end{array}\right]

\text { Find } A+2 B-3 C

\text { If } A=\left[\begin{array}{cc} 0 & -1 \\ 1 & 2 \end{array}\right] \text { and } B=\left[\begin{array}{cc} 1 & 2 \\ -1 & 1 \end{array}\right]

Find the matrix X if:

(i) 3A + X = B

(ii) X – 3B = 2A

Solve the matrix equation

\left[\begin{array}{ll} 2 & 1 \\ 5 & 0 \end{array}\right]-3 X=\left[\begin{array}{cc} -7 & 4 \\ 2 & 6 \end{array}\right]

Find the values of a and b if

\left[\begin{array}{cc} a+3 & b^{2}+2 \\ 0 & -6 \end{array}\right]=\left[\begin{array}{cc} 2 a+1 & 3 b \\ 0 & b^{2}-5 b \end{array}\right]

\text { If } A=\left[\begin{array}{ll} 3 & 5 \\ 4 & -2 \end{array}\right] \text { and } B=\left[\begin{array}{l} 2 \\ 4 \end{array}\right], \text { is the product } A B \text { possible } ? \text { Give a reason. If yes, } \text { find } \mathrm{AB} \text { . }

\text { If } A=\left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right], B=\left[\begin{array}{cc} 1 & -1 \\ -3 & 2 \end{array}\right], \text { find } A B \text { and } B A, \text { Is } A B=B A ?

\text { Find } a, b, c \text { and } d \text { if } 3\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]=\left[\begin{array}{cc} 4 & a+b \\ c+d & 3 \end{array}\right]+\left[\begin{array}{cc} a & 6 \\ -1 & 2 d \end{array}\right]

\text { If } P=\left[\begin{array}{cc} 4 & 6 \\ 2 & -8 \end{array}\right], Q=\left[\begin{array}{cc} 2 & -3 \\ -1 & 1 \end{array}\right]. Find 2PQ.

\text { Find } x \text { if } Y=\left[\begin{array}{ll} 3 & 2 \\ 1 & 4 \end{array}\right] \text { and } 2 X+Y=\left[\begin{array}{cc} 1 & 0 \\ -3 & 2 \end{array}\right]

Given A=\left[\begin{array}{ll} 1 & 1 \\ 8 & 3 \end{array}\right], \text { evaluate } A^{2}-4 A

\text { If } A=\left[\begin{array}{ll} 3 & 7 \\ 2 & 4 \end{array}\right], B=\left[\begin{array}{ll} 0 & 2 \\ 5 & 3 \end{array}\right] \text { and } C=\left[\begin{array}{cc} 1 & -5 \\ -4 & 6 \end{array}\right], find AB - 5C.

If A=\left[\begin{array}{ll} 1 & 2 \\ 2 & 1 \end{array}\right] \text { and } B=\left[\begin{array}{ll} 2 & 1 \\ 1 & 2 \end{array}\right], find A(BA).

Given matrices:

A=\left[\begin{array}{ll} 2 & 1 \\ 4 & 2 \end{array}\right] \text { and } B=\left[\begin{array}{cc} 3 & 4 \\ -1 & -2 \end{array}\right], C=\left[\begin{array}{cc} -3 & 1 \\ 0 & -2 \end{array}\right]

Find the products of

(i) ABC

(ii) ACB and state whether they are equal.

Evaluate : \left[\begin{array}{cc} 4 \sin 30^{\circ} & 2 \cos 60^{\circ} \\ \sin 90^{\circ} & 2 \cos 0^{\circ} \end{array}\right]\left[\begin{array}{ll} 4 & 5 \\ 5 & 4 \end{array}\right]

If A=\left[\begin{array}{cc} -1 & 3 \\ 2 & 4 \end{array}\right], B=\left[\begin{array}{cc} 2 & -3 \\ -4 & -6 \end{array}\right], find the matrix AB + BA.

If A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right] \text { and } B=\left[\begin{array}{ll} 6 & 1 \\ 1 & 1 \end{array}\right], C=\left[\begin{array}{cc} -2 & -3 \\ 0 & 1 \end{array}\right]

Find each of the following and state if they are equal.

(i) CA + B

(ii) A + CB