# 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:

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

Given that

$\mathbit{A}=\left[\begin{array}{cc}-5& -3\\ 2& 0\end{array}\right]$ and $\mathbit{I}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$, the value of A3 is

The matrix $\left[A\right]=\left[\begin{array}{cc}2& 1\\ 4& -1\end{array}\right]$  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 $\stackrel{\mathbf{\to }}{\mathbf{x}}$ is a real vector ${\left[{x}_{1},{x}_{2}\right]}^{\tau }$ 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 ?

$\mathrm{det}\left[\begin{array}{cc}& \\ & \end{array}\right]$