Answer:
a=2 and b=2.
Step-by-step explanation:
The given matrix multiplication is
[tex]\begin{bmatrix}3&2\\ -1&0\end{bmatrix}\begin{bmatrix}-2\\ 4\end{bmatrix}[/tex]
We need to resulting vector matrix of this matrix multiplication.
[tex]\begin{bmatrix}3\left(-2\right)+2\cdot \:4\\ \left(-1\right)\left(-2\right)+0\cdot \:4\end{bmatrix}[/tex]
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}[/tex]
It is given that [tex]\begin{bmatrix}a\\ b\end{bmatrix}[/tex] is resulting matrix.
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}=\begin{bmatrix}a\\ b\end{bmatrix}[/tex]
On comparing both sides, we get
[tex]a=2,b=2[/tex]
Hence, a=2 and b=2.
