Question

Determine the value of the unknown in the given matrix equalities

(2 −1 x

4 7 0)

(x 3

−2 5

1 −4)

=

(4 −2

1 5 )

Answer 1

$$\begin{pmatrix} 2 & -1 & x \\ 4 & 7 & 0 \end{pmatrix}\begin{pmatrix} x & 3 \\ -2 & 5 \\ 1 & -4 \end{pmatrix}$$

$$=\begin{pmatrix} 2x+2+x & 6-5-4x \\ 4x-14 & 12+35 \end{pmatrix}$$

$$=\begin{pmatrix} 3x+2 & 1-4x \\ 4x-14 & 47 \end{pmatrix}$$

$$\begin{pmatrix} 3x+2 & 1-4x \\ 4x-14 & 47 \end{pmatrix}\not=\begin{pmatrix} 4 & -2 \\ 1 & 5 \end{pmatrix}, x\in \R$$

There is no solution.