GATE Questions & Answers of Matrix Algebra

What is the Weightage of Matrix Algebra in GATE Exam?

Total 8 Questions have been asked from Matrix Algebra topic of Linear Algebra subject in previous GATE papers. Average marks 1.62.

Two matrices A and B are given below:

A=pqrs; B=p2+q2pr+qspr+qsr2+s2

If the rank of matrix A is N, then the rank of matrix B is

Given that

A=-5-320 and I=1001, the value of A3 is

The matrix A=214-1  is decomposed into a product of a lower triangular matrix [L] and an upper triangular matrix [U]. The properly decomposed [L] and [U] matrices respectively are

If the rank of a (5X6) matrix Q is 4, then which one of the following statement is correct ?

A is a m x n full rank matrix with m>n and I is identity matrix. Let matrix A+=(ATA)-1AT,Then, which one of the following statement is FALSE ?

Let P be a 2 X 2 real orthogonal matrix and x is a real vector x1,x2τ with length $\style{font-size:14px}{\parallel\overrightarrow x\parallel=\left(x_1^2+x_2^2\right)^\frac12.}$ Then, which one of the following statements is correct ?

x = [x1 x2 ... xn]T is an n-tuple nonzero vector. The n×n matrix  V=xx T

Let x and y be two vectors in a 3 dimensional space and <x, y> denote their dot product. Then the determinant

det<x,x><x,y><y,x><y,y>