Question

. Determine the value of the unknown in the given matrix equalities

(i)

(5 −2

−4 3 )+

(x y

w z)

=

(2 −1

3 6 )

Answer 1

$$\begin{pmatrix} 5 & -2 \\ -4 & 3 \end{pmatrix}+\begin{pmatrix} x & y \\ w & z \end{pmatrix}=\begin{pmatrix} 2 & -1 \\ 3 & 6 \end{pmatrix}$$

$$\begin{pmatrix} 5+x & -2+y \\ -4+w &3+z \end{pmatrix}=\begin{pmatrix} 2 & -1 \\ 3 & 6 \end{pmatrix}$$

$$5+x=2=>x=-3$$

$$-2+y=-1=>y=1$$

$$-4+w=3=>w=7$$

$$3+z=6=>z=3$$

$$\begin{pmatrix} x & y \\ w & z \end{pmatrix}=\begin{pmatrix} -3 & 1 \\ 7 & 3 \end{pmatrix}$$