1
GATE CSE 2024 Set 2
MCQ (More than One Correct Answer)
+2
-0.66

Let A be an n × n matrix over the set of all real numbers ℝ. Let B be a matrix obtained from A by swapping two rows. Which of the following statements is/are TRUE?

A

The determinant of B is the negative of the determinant of A

B

If A is invertible, then B is also invertible

C

If A is symmetric, then B is also symmetric

D

If the trace of A is zero, then the trace of B is also zero

2
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0.66

Let A be any n x m matrix, where m > n. Which of the following statements is/are TRUE about the system of linear equations Ax = 0?

A

There exist at least m - n linearly independent solutions to this system

B

There exist m - n linearly independent vectors such that every solution is a linear combination of these vectors

C

There exists a non-zero solution in which at least m - n variables are 0

D

There exists a solution in which at least n variables are non-zero

3
GATE CSE 2021 Set 1
Numerical
+2
-0.67

Consider the following matrix.

$$\left( {\begin{array}{*{20}{c}} 0&1&1&1\\ 1&0&1&1\\ 1&1&0&1\\ 1&1&1&0 \end{array}} \right)$$

The largest eigenvalue of the above matrix is ______

4
GATE CSE 2020
+2
-0.67
Let A and B be two n$$\times$$n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements,

I. rank(AB) = rank(A) rank(B)
II. det(AB) = det(A) det(B)
III. rank(A + B) $$\le$$ rank(A) + rank(B)
IV. det(A + B) $$\le$$ det(A) + det(B)

Which of the above statements are TRUE?
A
I and II only
B
II and III only
C
I and IV only
D
III and IV only
GATE CSE Subjects
EXAM MAP
Medical
NEET