# If and find(i) X + Y(ii) 2X – 3Y(iii) A matrix Z such that X + Y + Z is a zero matrix.

Addition or subtraction of matrices is possible only if the matrices are of same order.

That is,

If A and B are two matrices and if they are needed to be added, then if order of A is m × n, order of B must be m × n.

We have matrices X and Y, where

We know what order of matrix is,

If a matrix has M rows and N columns, the order of matrix is M × N.

(i). We need to find the X + Y.

Let us first determine order of X and Y.

Order of X:

Number of rows = 2

M = 2

Number of columns = 3

N = 3

Then, order of matrix X = M × N

Order of matrix X = 2 × 3

Order of Y:

Number of rows = 2

M = 2

Number of columns = 3

N = 3

Then, order of matrix Y = M × N

Order of matrix Y = 2 × 3

Since, order of matrix X = order of matrix Y

Matrices X and Y can be added.

So,

Thus, .

(ii). We need to find 2X – 3Y.

Let us calculate 2X.

We have,

Then, multiplying by 2 on both sides, we get

Also,

Multiplying by 3 on both sides, we get

Now subtract 3Y from 2X.

Thus, .

(iii). We need to find matrix Z, such that X + Y + Z is a zero matrix.

That is,

X + Y + Z = 0

Or,

Z = -X – Y

Or,

Z = -(X + Y)

We have already found X + Y in part (i).

So, from part (i):

Then,

Thus, .

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