Let A=pmatrix111pmatrix and B=pmatrix9^2&-10^2&11^212^2&13^2&-14^2-15^2&16^2&17^2pmatrix.

Question

Let $A=\begin{pmatrix}1\1\1\end{pmatrix}$ and $B=\begin{pmatrix}9^2&-10^2&11^2\12^2&13^2&-14^2\-15^2&16^2&17^2\end{pmatrix}$. Then the value of $A^TBA$ is:

Accepted Answer

$A^TBA=\begin{pmatrix}1&1&1\end{pmatrix}B\begin{pmatrix}1\1\1\end{pmatrix}$ is the sum of all entries of $B$:
$$\big(9^2-10^2+11^2\big)+\big(12^2+13^2-14^2\big)+\big(-15^2+16^2+17^2\big).$$

$$=(81-100+121)+(144+169-196)+(-225+256+289)=102+117+320=539.$$

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