1
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

For a given vector $${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$, the vector normal to the plane defined by $${w^T}x = 1$$ is

A
$${[\matrix{ { - 2} & { - 2} & 2 \cr } ]^T}$$
B
$${[\matrix{ 3 & 0 & { - 1} \cr } ]^T}$$
C
$${[\matrix{ 3 & 2 & 1 \cr } ]^T}$$
D
$${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$
2
GATE EE 2023
MCQ (Single Correct Answer)
+1
-0.33

In the figure, the vectors u and v are related as : Au = v by a transformation matrix A. The correct choice of A is

GATE EE 2023 Engineering Mathematics - Linear Algebra Question 7 English

A
$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr { - {3 \over 5}} & {{4 \over 5}} \cr } } \right]$$
B
$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$
C
$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$
D
$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & { - {4 \over 5}} \cr } } \right]$$
3
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a 3 $$\times$$ 3 matrix A whose (i, j)-th element, ai,j = (i $$-$$ j)3. Then the matrix A will be

A
symmetric
B
skew-symmetric
C
unitary
D
null
4
GATE EE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & 0 & {{3 \over 2}} \cr } } \right]$$ has three distinct eigen values and one of its eigen vectors is $$\left[ {\matrix{ 1 \cr 0 \cr 1 \cr } } \right].$$ Which one of the following can be another eigen vector of $$A$$?
A
$$\left[ {\matrix{ 0 \cr 0 \cr { - 1} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 1} \cr 0 \cr 0 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 \cr 0 \cr { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 \cr { - 1} \cr 1 \cr } } \right]$$
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