1
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 __________.

A
a unique solution for x
B
infinitely many solutions for x
C
no solutions for x
D
exactly two solutions for x
2
GATE ECE 2021
Numerical
+1
-0
If the vectors (1.0, $$-$$1.0, 2.0), (7.0, 3.0, x) and (2.0, 3.0, 1.0) in R3 are linearly dependent, the value of x is _______.
Your input ____
3
GATE ECE 2020
MCQ (Single Correct Answer)
+1
-0.33

If $\mathbf{v}_{\mathbf{1}}, \mathbf{v}_{\mathbf{2}} \ldots \mathbf{v}_{\mathbf{6}}$ are six vectors in $\mathbb{R}^4$, which one of the statements is FALSE?

A

Any four of these vectors form a basis for $\mathbb{R}^4$.

B

It is not necessary that these vectors span $\mathbb{R}^4$.

C

If $\left\{\mathbf{v}_1, \mathbf{v}_3, \mathbf{v}_5, \mathbf{v}_6\right\}$ spans $\mathbb{R}^4$, then it forms a basis of $\mathbb{R}^4$.

D

These vectors are not linearly independent.

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 _______.
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