If A is a syymmetric matrix and B is a skew-symmetrix matrix such that A+B=\begin{bmatrix} 2 &3 \\5 &-1 \end{bmatrix}, then AB is equal to : 


 

  • Option 1)

    \begin{bmatrix} -4 &-2 \\ -1 &4 \end{bmatrix}

  • Option 2)

    \begin{bmatrix} 4 &-2 \\ -1 & -4 \end{bmatrix}

  • Option 3)

    \begin{bmatrix} 4 &-2 \\ 1 &-4 \end{bmatrix}

  • Option 4)

    \begin{bmatrix} -4 &2 \\ 1 & 4 \end{bmatrix}

 

Answers (1)

A is symmetric matrix 

{A}'=A

B is skew-symmetrix

{B}'=-B

A+B=\begin{bmatrix} 2 &3 \\5 &-1 \end{bmatrix}\cdots \cdots (1)

{A}'+{B}'=\begin{bmatrix} 2 &5 \\3 &-1 \end{bmatrix}

A-B=\begin{bmatrix} 2 &5 \\3 &-1 \end{bmatrix}\cdots \cdots (2)

(1) + (2) 

A=\begin{bmatrix} 2 &4 \\4 &-1 \end{bmatrix}, B=\begin{bmatrix} 0 &-1 \\ 1 &0 \end{bmatrix}

AB=\begin{bmatrix} 4& -2\\ -1 &-4 \end{bmatrix}


Option 1)

\begin{bmatrix} -4 &-2 \\ -1 &4 \end{bmatrix}

Option 2)

\begin{bmatrix} 4 &-2 \\ -1 & -4 \end{bmatrix}

Option 3)

\begin{bmatrix} 4 &-2 \\ 1 &-4 \end{bmatrix}

Option 4)

\begin{bmatrix} -4 &2 \\ 1 & 4 \end{bmatrix}

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