If x[23]+y[−11]=[105], then find the values of x and y.
If x[23]+y[−11]=[105]⇒[2x+y(−1)3x+y]=[105]
By definition of equality of matrix as the given matrices are equal, their corresponding elements are equal. Comparing the corresponding elements, we get
2x-y=10.........(i)
and 3x+y =5 .......(ii)
Adding Eqs. (i) and (ii), we get
5x=15⇒x=3
Substituting x=3 in Eq. (i), we get
2×3−y=10⇒y=6−10=−4