Question

solve for 50 points
Maths Matrices
class 12​

Answer 1

Question :

If X and Y are two given matrices

Find X+Y

Theory :

properties of Addition of matrices :

If A B and C are matrices of same order,then

1. Commutative law:A+B=B+A
2. Associative law : (A+B)+C = A+(B+C)
3. cancellation law
4. A+O = A , where is O isa zero matrix of the order of matrix A.
5. tr(A+B) = tr(A)+tr(B)

${\red{\boxed{\large{\bold{Note}}}}}$

Matrix addition and subtraction can be only possible when matrices are of same order.

Solution:

$X=\left[\begin{array}{ccc}3&1&-1\\5&-2&-3\end{array}\right]\quad\quad Y=\left[\begin{array}{ccc}2&1&-1\\7&2&4\end{array}\right]\\\\\\\begin{aligned}X+Y&=\left[\begin{array}{ccc}3&1&-1\\5&-2&-3\end{array}\right]+\left[\begin{array}{ccc}2&1&-1\\7&2&4\end{array}\right]\\\\&=\left[\begin{array}{ccc}5&2&-2\\12&0&1\end{array}\right]\end{aligned}$

refer to the attachment.

Answer 2

Addition of Matrices :

If $A= (a_{ij}) _{m \times n} \: and \: B = (b_{ij})_{m \times n}$

are two matrices of the same order then their sum A+B is matrix whose each element is the sum of corresponding elements of two matrices.

$i.e \: A+ B = (a _{ij} + b_{ij})_{mn}$

Note :

Matrix addition and subtraction can be possible only when matrices of same order.

Solution :

$X=\left[\begin{array}{ccc}3&1&-1\\5&-2&-3\end{array}\right]\quad\quad Y=\left[\begin{array}{ccc}2&1&-1\\7&2&4\end{array}\right]\\\\\\\begin{aligned}X+Y&=\left[\begin{array}{ccc}3&1&-1\\5&-2&-3\end{array}\right]+\left[\begin{array}{ccc}2&1&-1\\7&2&4\end{array}\right]\\\\&=\left[\begin{array}{ccc}5&2&-2\\12&0&1\end{array}\right]\end{aligned}$