## Related questions with answers

Question

Find $(a)$ $A^TA$ and $(b)$ $AA^T$. Show that each of these products is symmetric.

$A=$

$\begin{bmatrix} 4 & -3 & 2 & 0 \\ 2 & 0 & 11 &-1 \\ -1 & -2 & 0 & 3 \\ 14 & -2 & 12 & -9 \\ 6 &8 & -5 &4 \end{bmatrix}$

Solutions

VerifiedSolution A

Solution B

Answered 1 year ago

Step 1

1 of 6The transpose of a matrix is formed by writing its rows as columns. This means that each element with indices $\left (i,j \right )$ in the original matrix $A$ of size $m\times n$ will be at the place with indices $\left ( j,i\right )$ in the new matrix $A^T$ of size $n\times m.$

A matrix $A$ is called symmetric if the following is true:

$A=A^T.$

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