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  • Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 64 math

Need solution for RD Sharma maths class 12 chapter Algebra of matrices exercise 4.3 question 64 math

 

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Answer: a=5, b=4 and order of XY and YX are not the same and they are not equal but both are square matrices

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: Matrix X has a+b rows and a+2 columns. Matrix y has b+1 rows and a+3 column both the matrices XY and  YX exist.

So, order of matrix X=(a+b)(a+2) order of matrix Y=(b+1)(a+3)

Multiplication of matrix YX exists, when the number of columns of Y is equal to the number of rows of X.

\begin{array}{l} \text { So, } Y_{(b+1) \times(a+3)}{X}_{(a+b) \times(a+2)} \text { exists }\\\\ a+3=a+b\\\\ b=3 \quad \ldots (i) \end{array}

Multiplication of matrix XY exists, when the number of columns of X is equal to the number of rows of Y.

\begin{array}{l} X_{(a+b) \times(a+2)} Y_{(b+1) \times(a+3)} \\\\ (a+2)=(b+1) \\\\ a-b=-1 \\\\ a-3=-1 \quad \text { [ using (i) ] }\\\\ a=2 ... (ii)\\ \end{array}

So order of  X=(a+b) \times(a+2)

                           \\ \qquad \begin{aligned} &=(2+3) \times(2+2) \\ &=5 \times 4 \\ &=(3+1) \times(2+3) \\ &=4 \times 5 \end{aligned}


Order of   Y=(b+1) \times(a+3)

                        \\ \begin{array}{l} \\=(3+1) \times(2+3) \\ =4 \times 5 \\ \end{array}

Order of   X_{5 \times 4} Y_{4 \times 5}=5 \times 5 \\

Order of    Y_{4 \times 5} X_{5 \times 4}=4 \times 4

So, order of XY and YX are not same and they are not equal but both XY and YX are square matrices.

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