Mixing Until One Weight Disappears

Two training runs each produce a $3 \times 3$ weight matrix:

$A = \begin{bmatrix} 3 & -1 & 5 \\ 4 & 2 & 6 \\ -2 & 7 & 0 \end{bmatrix}, \qquad B = \begin{bmatrix} -5 & 8 & 1 \\ 3 & -4 & -2 \\ 6 & 2 & 6 \end{bmatrix}$

Rather than pick one, an engineer blends them into a single matrix using a mixing weight $t$:

$W = (1 - t)\,A + t\,B$

She wants the connection stored at row 2, column 3 to switch off completely — that is, she needs $W_{2,3} = 0$.

Find the value of $t$ that achieves this, and with that same $t$ report the sum of all nine entries of $W$.

Round your answer to two decimal places.