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
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?
4
GATE ECE 2018
Numerical
+1
-0
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 ____
Questions Asked from Marks 1
GATE ECE 2025 (1) GATE ECE 2024 (1) GATE ECE 2023 (1) GATE ECE 2022 (1) GATE ECE 2018 (2) GATE ECE 2017 Set 1 (2) GATE ECE 2016 Set 2 (1) GATE ECE 2016 Set 1 (1) GATE ECE 2016 Set 3 (1) GATE ECE 2015 Set 2 (1) GATE ECE 2015 Set 1 (2) GATE ECE 2015 Set 3 (1) GATE ECE 2014 Set 3 (1) GATE ECE 2014 Set 2 (3) GATE ECE 2014 Set 1 (3) GATE ECE 2013 (2) GATE ECE 2012 (1) GATE ECE 2011 (1) GATE ECE 2010 (1) GATE ECE 2008 (2) GATE ECE 2006 (2) GATE ECE 2000 (1) GATE ECE 1998 (1) GATE ECE 1994 (2)
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics