GATE Questions & Answers of Linear Algebra Civil Engineering

The matrix $ \begin{pmatrix}2&-4\\4&-2\end{pmatrix} $ has

The matrix P is the inverse of a matrix Q. If I denotes the identitiy matrix, which one of the following option is correct?

The number of parameters in the univariate exponential and Gaussian distributions, respectively, are

Consider the matrix $\style{font-family:'Times New Roman'}{\begin{bmatrix}5&-1\\4&1\end{bmatrix}}$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Consider following simultaneous equations (with $ \begin{array}{l}c_1\\\end{array} $ and $ \begin{array}{l}c_2\\\end{array} $ being constants):

$ \begin{array}{l}3\;x_1+2\;x_2=c_1\\4\;x_1+x_2=c_2\end{array} $

The characteristic equation for these simultaneous equation is

If $ \mathbf A=\begin{bmatrix}1&5\\6&2\end{bmatrix} $ and $ \mathbf B=\begin{bmatrix}3&7\\8&4\end{bmatrix},\boldsymbol A\boldsymbol B^T $ is equal to

If the entries in each column of a square matrix Μ add up to 1, then an eigenvalue of Μ is

Consider the following linear system.

x+2y-3z=a

2x+3y+3z=b

5x+9y-6z=c

This system is consistent if $a, b$ and $c$ satisfy the equation

For what value of p the following set of equation will have no solution ?

$ \begin{array}{l}2\mathrm x+3\mathrm y=5\\3\mathrm x+\mathrm{py}=10\end{array} $

The smallest and largest Eigen values of the following matrix are:

3-224-462-35

Let $ A=\lbrack a_{ij}\rbrack,1\leq i,j<n $ with $ n\geq3 $ and $ a_{ij}=i.j. $ The rank of $ A $ is :

The two Eigen Values of the matrix 211p have a ratio of 3:1 for p = 2. What is another value of p for which the Eigen values have the same ratio of 3:1?

Given the matrices J=321242126 and K=12-1,the product KT JK is _________.

The sum of Eigen values of the matrix, [M] is

where M=215650795655150835485355550

The determinant of matrix 0123103023013012 is ____________

The rank of the matrix 6044-21481814-140-10 is _______________

What is the minimum number of multiplications involved in computing the matrix product PQR? Matrix P has 4 rows and 2 columns, matrix Q has 2 rows and 4 columns, and matrix R has 4 rows and 1 column. __________

The eigen values of matrix 9558 are

[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose.The sum and differene of these matrices are defined as [s]=[A]+[A]T and [D]=[A]-[A]T,respectively.Which of the following statements is true?

The inverse of the matrix  3+2ii-i3-2i is

A square matrix B is skew-symmetric if

The product of matrices PQ-1 P is

The value of $\int\limits_0^3\int\limits_0^x\left(6-x-y\right)dx\;dy$ is

The Eigen values of the matrix P=452-5 are

The following simultaneous equations

x+y+z=3
x+2y+3z=4
x+4y+kz=6

will NOT have a unique solution for k equal to

The minimum and the maximum eigen velue of the matrix 113151311 are -2 and 6, respectively. What is the other eigen value?

For what values of α and β the following simultaneous equations have an infinite number of solutions?

x + y + z = 5;     x + 3y + 3z = 9;     x + 2y + αz = β

The inverse of the 2 × 2 matrix 1257 is