GATE EE 2024 | Linear Algebra Question 6 | Engineering Mathematics

GATE EE 2024

Numerical

-0

The sum of the eigenvalues of the matrix $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}^2$ is ______ (rounded off to the nearest integer).

Your input ____

GATE EE 2023

MCQ (Single Correct Answer)

-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

$${[\matrix{ { - 2} & { - 2} & 2 \cr } ]^T}$$

$${[\matrix{ 3 & 0 & { - 1} \cr } ]^T}$$

$${[\matrix{ 3 & 2 & 1 \cr } ]^T}$$

$${[\matrix{ 1 & 2 & 3 \cr } ]^T}$$

GATE EE 2023

MCQ (Single Correct Answer)

-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

$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr { - {3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

$$\left[ {\matrix{ {{4 \over 5}} & {{3 \over 5}} \cr {{3 \over 5}} & {{4 \over 5}} \cr } } \right]$$

$$\left[ {\matrix{ {{4 \over 5}} & { - {3 \over 5}} \cr {{3 \over 5}} & { - {4 \over 5}} \cr } } \right]$$

GATE EE 2022

MCQ (Single Correct Answer)

-0.33

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

symmetric

skew-symmetric

unitary

null

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