Question

If \left[\begin{array}{ccc}x-1&2&5-y\\0&z-1&7\\1&0&a-5\end{array}\right] = \left[\begin{array}{ccc}1&2&3\\0&4&7\\1&0&0\end{array}\right] then find the values of x, y z and a.

Answer 1

Answer: x=2,y=2,z=5,a=5

Solution:

$\left[\begin{array}{ccc}x-1&2&5-y\\0&z-1&7\\1&0&a-5\end{array}\right] = \left[\begin{array}{ccc}1&2&3\\0&4&7\\1&0&0\end{array}\right]$

since both matrix are equal ,so every element of 1st matrix is equal to that corresponding element in second matrix

By this way

$x - 1 = 1 \\ \\ x = 2 \\ \\ 5 - y = 3 \\ \\ - y = 3 - 5 \\ \\ y = 2$
$z - 1 = 4 \\ \\ z = 5$
$a - 5 = 0 \\ \\ a = 5$