Question

( [ x + 4 , t − 5 ] , [ t + 4 , x − 4 ] ) = ( [ y + 3 , z − 1 ] , [ y + 5 , − 2 ] )

Answer 1

Looks like these are equal matrices,

`\begin{bmatrix}x+4&t-5\\t+4&x-4\end{bmatrix}=\begin{bmatrix}y+3&z-1\\y+5&-2\end{bmatrix}`

Two (identically-sized) matrices are equal to each other if their entries in the same positions are equal. This means

`\begin{cases}x+4=y+3\\t-5=z-1\\t+4=y+5\\x-4=-2\end{cases}`

From the last equation we get
`x=2`. Then

`x+4=6=y+3\implies y=3`

`t+4=y+5=8\implies t=4`

`t-5=-1=z-1\implies z=0`