matrix

Matrix A has the eigenvalues 1, 2, and 3. The Trace of A² is

Matrix P is given as $P = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}$ The TRUE option is

Given: $\begin{bmatrix} 1 & 1 \\ 1 & 0 \\ 0 & 2 \end{bmatrix} \begin{Bmatrix} x_1 \\ x_2 \\ x_3 \end{Bmatrix} = \begin{Bmatrix} 0 \\ 0 \end{Bmatrix}$ The above system of equations...

A matrix is given as: $$\begin{bmatrix} 9 & 15 \\ 15 & 50 \end{bmatrix}$$ By performing Cholesky decomposition, $|L_{22}|$ of the lower triangular matrix is ________ (in integer).

The eigenvalues of $[A] = \begin{bmatrix} 2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5 \end{bmatrix}$ are $\lambda_1 = -1.547$, $\lambda_2 = 12.330$, and $\lambda_3 = 4.711$. The abs...

In the context of the given figure, which one of the following options correctly represents the entries in the blocks labelled (i), (ii), (iii), and (iv), respectively? N U F (i) 2...

Suppose $\lambda$ is an eigenvalue of matrix A and x is the corresponding eigenvector. Let x also be an eigenvector of the matrix B = A - 2I, where I is the identity matrix. Then,...

Let $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 3 \\ 1 & -2 & -3 \end{bmatrix}$ and $b = \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix}$. For Ax = b to be solvable, which one of the...

Pick the CORRECT eigen value(s) of the matrix [A] from the following choices. [A] = [[6, 8], [4, 2]]

For the matrix $[\mathrm{A}]$ given below, the transpose is $\qquad$ . $$ [A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right] $$

Pick the CORRECT eigen value(s) of the matrix $[\mathrm{A}]$ from the following choices. $$ [A]=\left[\begin{array}{ll} 6 & 8 \\ 4 & 2 \end{array}\right] $$

What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$?

What are the eigenvalues of the matrix $\begin{bmatrix} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 2 \end{bmatrix}$ ?

If M is an arbitrary real n x n matrix, then which of the following matrices will have non-negative eigenvalues?

For the matrix $[A] = \begin{bmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{bmatrix}$ which of the following statements is/are TRUE?

Cholesky decomposition is carried out on the following square matrix [A]. $[A] = \begin{bmatrix} 8 & -5 \\ -5 & a_{22} \end{bmatrix}$ Let $l_{ij}$ and $a_{ij}$ be the $(i,j)^{th}$...

For the matrix [A] = [1 2 3] [3 2 1] [3 1 2] which of the following statements is/are TRUE?

The components of pure shear strain in a sheared material are given in the matrix form: $\varepsilon = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$ Here, Trace($\varepsilon$) = 0...

Let y be a non-zero vector of size 2022 × 1. Which of the following statement(s) is/are TRUE?

The rank of matrix $\begin{bmatrix} 1 & 2 & 2 & 3 \\ 3 & 4 & 2 & 5 \\ 5 & 6 & 2 & 7 \\ 7 & 8 & 2 & 9 \end{bmatrix}$ is

The rank of the matrix $\begin{bmatrix} 5 & 0 & -5 & 0 \\ 0 & 2 & 0 & 1 \\ -5 & 0 & 5 & 0 \\ 0 & 1 & 0 & 2 \end{bmatrix}$ is

If A is a square matrix then orthogonality property mandates

The smallest eigenvalue and the corresponding eigenvector of the matrix [[2, -2], [-1, 6]], respectively, are

Consider the system of equations $\begin{bmatrix} 1 & 3 & 2 \\ 2 & 2 & -3 \\ 4 & 4 & -6 \\ 2 & 5 & 2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix}...

The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is

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

Which one of the following matrices is singular?

For the given orthogonal matrix Q, Q = [3/7 2/7 6/7; -6/7 3/7 2/7; 2/7 6/7 -3/7]. The inverse is

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

The rank of the following matrix is $\begin{pmatrix} 1 & 1 & 0 & -2 \ 2 & 0 & 2 & 2 \ 4 & 1 & 3 & 1 \end{pmatrix}$

Consider the matrix $\begin{bmatrix} 5 & -1 \ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Consider the matrix $$\left[ {\matrix{ 5 & { - 1} \cr 4 & 1 \cr } } \right].$$ Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?

Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$ The rank of $$A$$ is :

The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$

The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen va...

The rank of the matrix $$\left[ {\matrix{ 6 & 0 & 4 & 4 \cr { - 2} & {14} & 8 & {18} \cr {14} & { - 14} & 0 & { - 10} \cr } } \right]$$ is

The determinant of matrix $$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 & 0 & 1 & 2 \cr } } \right]$$ is

The eigen values of matrix $$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$ are

The eigenvalues of the matrix $$\left[ P \right] = \left[ {\matrix{ 4 & 5 \cr 2 & { - 5} \cr } } \right]$$ are

For a given matrix $$A = \left[ {\matrix{ 2 & { - 2} & 3 \cr { - 2} & { - 1} & 6 \cr 1 & 2 & 0 \cr } } \right],$$ one of the eigen value is $$3.$$ The other two eigen values are

The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are

Eigen values of the following matrix are $$\left[ {\matrix{ { - 1} & 4 \cr 4 & { - 1} \cr } } \right]$$

Obtain the eigen values and eigen vectors of $$A = \left[ {\matrix{ 8 & -4 \cr 2 & { 2 } \cr } } \right].$$