## Related questions with answers

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why.

$\begin{bmatrix} x & 2y & z \\ r/4 & -s & -5t \end{bmatrix} = \begin{bmatrix} -2 & 10 & -9 \\ 12 & -4 & 5 \end{bmatrix}$

Solution

Verified$\begin{bmatrix}x & 2y & z\\r/4 & -s & -5t\end{bmatrix} = \begin{bmatrix}-2 & 10 & -9\\12 & -4 & 5\end{bmatrix} \\$

Two matrices are said to be equal if and only if they are identical. That is, they must have the same number of columns, the same number of rows, and the elements must respectively be equal. $\\$ This two matrices have the same number of columns and rows so in order to be equal element must be equal respectively so$

x = -2

2y = 10

y = 10/2

y = 5

z = -9

r/4 = 12

r = 4 \cdot 12

r = 48

-s = -4

(-1)\cdot s = -4

s = $\dfrac{-4}{-1}$ = 4

-5t = 5

t = $\dfrac{5}{-5}$ = -1

$

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