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Recent questions tagged matrices

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GATE Civil 2023 Set 2 | Question: 15
For the matrix$[A]=\left[\begin{array}{ccc}1 & -1 & 0 \\-1 & 2 & -1 \\0 & -1 & 1\end{array}\right]$which of the following statements is/are TRUE?$[A]\{x\}=\{b\}$ has a un...
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GATE Civil 2021 Set 2 | Question: 2
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$1$$2$$3$$4$
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GATE Civil 2021 Set 2 | Question: 4
If $\text{A}$ is a square matrix then orthogonality property mandates$AA^{T}=I$$AA^{T}=0$$AA^{T}=A^{-1}$$AA^{T}=A^{2}$
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GATE Civil 2021 Set 2 | Question: 27
The smallest eigenvalue and the corresponding eigenvector of the matrix $\begin{bmatrix} 2 & -2 \\ -1 & 6 \end{bmatrix}$, respectively, are$1.55$ and $\begin{Bmatrix} 2.0...
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GATE Civil 2021 Set 1 | Question: 1
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$1$$2$$3$$4$
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GATE Civil 2021 Set 1 | Question: 2
If $P=\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q=\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^{T}\:P^{T}$ is$\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatri...
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GATE2020-CE-1-40
Consider the system of equations$$\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} 1 \\ 1 ...
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GATE2020 CE-2-27
A $4 \times 4$ matrix $[P]$ is given below$$[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$$The eigen values of $[P]$ are $0, 3, 6,...
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GATE2017 CE-2-28
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to$\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{b...
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GATE2019 CE-2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & -2 & -6 \end{bmatrix}^T$ is$\sqrt{12}$$\sqrt{24}$$\sqrt{48}$$\sqrt{56}$
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GATE2019 CE-2: 35
The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is $\begin{bmatrix} 10 & -4 & -9 \\ -15 & 4 & 14 \\ 5 & -1 & -6 \end{bmatrix...
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GATE2016-1-3
If the entries in each column of a square matrix $M$ add up to $1$, then an eigenvalue of $M$ is$4$$3$$2$$1$
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GATE2017 CE-1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct?$PQ=I$ but $QP \neq I$$QP=I$ but $PQ \neq...
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GATE2017 CE-1: 28
Consider the matrix $\begin{bmatrix} 5 & -1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?Eig...
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GATE2015-2-5
Let $A=[a_{ij}], \: 1 \leq i, j \leq n$ with $n \geq 3$ and $a_{ij}=i \cdot j$. The rank of $A$ is:$0$$1$$n-1$$n$
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GATE2015-2-28
The two Eigen values of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & p \end{bmatrix}$ have a ratio of $3:1$ for $p=2$. What is another value of $p$ for which the Eigen values...
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GATE2015-1-26
The smallest and largest Eigen values of the following matrix are:$\begin{bmatrix} 3 & -2 & 2 \\ 4 & -4 & 6 \\ 2 & -3 & 5 \end{bmatrix}$$1.5$ and $2.5$$0.5$ and $2.5$$1.0...
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GATE2014-2-28
The rank of the matrix $\begin{bmatrix} 6 & 0 & 4 & 4 \\ -2 & 14 & 8 & 18 \\ 14 & -14 & 0 & -10 \end{bmatrix}$ is _________
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GATE2014-2-2
The determinant of matrix $\begin{bmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 0 \\ 2 & 3 & 0 & 1 \\ 3 & 0 & 1 & 2 \end{bmatrix}$ is ________
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GATE2014-1-2
Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _...
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GATE2014-1-4
The sum of Eigen values of the matrix, $[M]$ iswhere $[M] = \begin{bmatrix} 215 & 650 & 795 \\ 655 & 150 & 835 \\ 485 & 355 & 550 \end{bmatrix}$$915$$1355$$1640$$2180$
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GATE Civil 2013 | Question: 2
What is the minimum number of multiplications involved in computing the matrix product $PQR?$ Matrix P has $4$ rows an $2$ columns, matrix $Q$ has $2$ rows and $4$ column...
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GATE Civil 2012 | Question: 28
The eigenvalues of matrix $\begin{bmatrix} 9 & 5 \\ 5 & 8 \end{bmatrix}$ are$-2.42$ and $6.86$$3.48$ and $13.53$$4.70$ and $6.86$$6.86$ and $9.50$
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GATE2018 CE-2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$$1$$2$$3$$4$
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GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ hasreal eigenvalues and eigenvectorsreal eigenvalues but complex eigenvectorscomplex eigenvalues but real eige...
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GATE2018 CE-1: 2
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ -6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & -3/7 \end{bmatrix}$ The inverse is$\begin{bmatrix} 3/7 & 2/7 &...
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GATE2018 CE-1: 1
Which one of the following matrices is singular?$\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$$\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$$\begin{bmatrix} 2 & 4\\...
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