Engineering Questions with Answers - Multiple Choice Questions

# Linear Algebra MCQ – Rank of Matrix in Row Echelon Form

1 - Question

Write Matrix corresponding to the following linear transformations.
y1=2x1-x2-x3
y2=3x3
y3=x1+x2
a) ⎡⎣⎢201101130⎤⎦⎥
b) ⎡⎣⎢201100130⎤⎦⎥
c) ⎡⎣⎢201101131⎤⎦⎥
d) ⎡⎣⎢201111130⎤⎦⎥

Explanation: In the given question,
We know that Linear Transformation is given by,
⎡⎣⎢y1y2y3⎤⎦⎥⎡⎣⎢201101130⎤⎦⎥⎡⎣⎢x1x2x3⎤⎦⎥

Thus, the matrix for linear transformation is
⎡⎣⎢201101130⎤⎦⎥.

2 - Question

Which of the following Linear Transformations is not correct for the given matrix?
⎡⎣⎢112201310⎤⎦⎥
a) x1=1y1-3y2-3y3
b) x1=1y1-2y2-3y3
c) x2=-1y1+1y3
d) x3=2y1+y2

Explanation: In the given question,
X=⎡⎣⎢112201310⎤⎦⎥Y
Thus,
x1=1y1-2y2-3y3
x2=-1y1+1y3
x3=2y1+y2.

3 - Question

For the linear transformation, X=⎡⎣⎢211110122⎤⎦⎥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)

Explanation: In the given question,
X=(1, 2, -1)
⎡⎣⎢121⎤⎦⎥⎡⎣⎢211110122⎤⎦⎥⎡⎣⎢y1y2y3⎤⎦⎥

y1– 2y3=-1
y2+4y3=3
y3=0
Thus Y (-1, 3, 0).