Linear Algebra Questions and Answers – Rank of Matrix in Row Echelon Form

This set of Linear Algebra Questions and Answers for Freshers focuses on “Rank of Matrix in Row Echelon Form”.

1. Write Matrix corresponding to the following linear transformations.
a) \(\begin{bmatrix}2&-1&-1\\0&0&3\\1&1&0\end{bmatrix}\)
b) \(\begin{bmatrix}2&-1&-1\\0&0&3\\1&0&0\end{bmatrix}\)
c) \(\begin{bmatrix}2&-1&-1\\0&0&3\\1&1&1\end{bmatrix}\)
d) \(\begin{bmatrix}2&-1&-1\\0&1&3\\1&1&0\end{bmatrix}\)

View Answer

Answer: a
Explanation: In the given question,
We know that Linear Transformation is given by,

Thus, the matrix for linear transformation is

2. Which of the following Linear Transformations is not correct for the given matrix?
a) x1=1y1-3y2-3y3
b) x1=1y1-2y2-3y3
c) x2=-1y1+1y3
d) x3=2y1+y2
View Answer

Answer: a
Explanation: In the given question,

3. 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)
View Answer

Answer: d
Explanation: In the given question,
X=(1, 2, -1)

y1– 2y3=-1
Thus Y (-1, 3, 0).

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