Question

Which among the following is the new matrix after applying the elementary operation C1→4C1 on the matrix A=\(\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}\)?

(a) \(\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}\)

(b) \(\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}\)

(c) \(\begin{bmatrix}20&8\\4&2\\12&-4\end{bmatrix}\)

(d) \(\begin{bmatrix}20&8\\-4&2\\12&4\end{bmatrix}\)

The question was asked in examination.

My question comes from Elementary Operation (Transformation) of a Matrix topic in portion Matrices of Mathematics – Class 12

Answer 1

Correct choice is (b) \(\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}\)

The best I can explain: Given matrix A=\(\begin{bmatrix}5&8\\-1&2\\3&-4\end{bmatrix}\)

Applying the column operation, C1→4C1 we get

\(\begin{bmatrix}4(5)&8\\4(-1)&2\\4(3)&-4\end{bmatrix}\)=\(\begin{bmatrix}20&8\\-4&2\\12&-4\end{bmatrix}\)