For a square matrix A,if A = B + frac{C}{2},w | vedclass

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(A) We know that any square matrix $A$ can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix: $A = \frac{A + A^{\prime}}{2} +

Vedclass · Accepted Answer

$A + A^{\prime}$

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(A) We know that any square matrix $A$ can be expressed as the sum of a symmetric matrix and a skew-symmetric matrix: $A = \frac{A + A^{\prime}}{2} + \frac{A - A^{\prime}}{2}$. Here,$\frac{A + A^{\prime}}{2}$ is a symmetric matrix and $\frac{A - A^{\prime}}{2}$ is a skew-symmetric matrix. Given $A = B + \frac{C}{2}$,where $B$ is skew-symmetric and $C$ is symmetric. Comparing the two expressions,we identify $B = \frac{A - A^{\prime}}{2}$ and $\frac{C}{2} = \frac{A + A^{\prime}}{2}$. Multiplying by $2$,we get $C = A + A^{\prime}$. Therefore,the correct option is $A$.

For a square matrix $A$,if $A = B + \frac{C}{2}$,where $B$ is a skew-symmetric matrix and $C$ is a symmetric matrix,then $C = $ . . . . . . .

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