1
GATE ECE 2023
MCQ (Single Correct Answer)
+1
-0.33
Let the sets of eigenvalues and eigenvectors of a matrix B be $$\{ {\lambda _k}|1 \le k \le n\} $$ and $$\{ {v_k}|1 \le k \le n\} $$, respectively. For any invertible matrix P, the sets of eigenvalues and eigenvectors of the matrix A, where $$B = {P^{ - 1}}AP$$, respectively, are
2
GATE ECE 2022
MCQ (Single Correct Answer)
+1
-0.33
Consider a system of linear equations Ax = b, where
$$A = \left[ {\matrix{ 1 \hfill & { - \sqrt 2 } \hfill & 3 \hfill \cr { - 1} \hfill & {\sqrt 2 } \hfill & { - 3} \hfill \cr } } \right]$$, $$b = \left[ {\matrix{ 1 \cr 3 \cr } } \right]$$
This system is equations admits __________.
3
GATE ECE 2018
Numerical
+1
-0.33
Consider matrix $$A = \left[ {\matrix{
k & {2k} \cr
{{k^2} - k} & {{k^2}} \cr
} } \right]$$ and
vector $$X = \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$.
The number of distinct real values of k for which the equation AX = 0 has infinitely many solutions is _______.
vector $$X = \left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right]$$.
The number of distinct real values of k for which the equation AX = 0 has infinitely many solutions is _______.
Your input ____
4
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Let
M
be a real
4 $$ \times $$ 4
matrix. Consider the following statements :
S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?
S1: M has 4 linearly independent eigenvectors.
S2: M has 4 distinct eigenvalues.
S3: M is non-singular (invertible).
Which one among the following is TRUE?
Questions Asked from Linear Algebra (Marks 1)
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GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics