Question

For the linear transformation, X=\(\begin{bmatrix}2&1&1\\1&1&2\\1&0&-2\end{bmatrix}\)Y, find the Y co-ordinates for (1, 2, -1) in X.

(a) (0, -2, 0)

(b) (-1, 3, 1)

(c) (-1, -2, 0)

(d) (-1, 3, 0)

I got this question in unit test.

Origin of the question is Rank of Matrix in Row Echelon Form topic in chapter Matrices of Engineering Mathematics

Answer 1

The correct choice is (d) (-1, 3, 0)

For explanation I would say: In the given question,

X=(1, 2, -1)

\(\begin{bmatrix}1\\2\\-1\end{bmatrix}\begin{bmatrix}2&1&1\\1&1&2\\1&0&-2\end{bmatrix}\begin{bmatrix}y1\\y2\\y3\end{bmatrix}\)  

y1– 2y3=-1

y2+4y3=3

y3=0

Thus Y (-1, 3, 0).