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Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \textbf{Year}& \textbf{2026 - 1}& \textbf{2026 - 2}& \textbf{2025 - 1}& \textbf{2025 - 2}& \textbf{2024 - 1}& \textbf{2024 - 2}& \textbf{2023}& \textbf{2022}& \textbf{2021 - 1}& \textbf{2021 - 2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}\\\hline \textbf{1 Mark Count}&2&1&1&2&1&0&2&1&0&1&0&1.1&2\\\hline \textbf{2 Marks Count}&0&1&1&1&1&1&0&2&1&1&0&0.9&2\\\hline \textbf{Total Marks}&2&3&3&4&3&2&2&5&2&3&\bf{2}&\bf{2.9}&\bf{5}\\\hline \end{array}}}$$

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Recent questions in Linear Algebra

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1 1 answer
61
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GATE DA LA Practice Problem
Select the correct statement(s) regarding the existence of real matrices:A) There exists a matrix whose nullspace is $\text{span}\left\{ \begin{bmatrix} 1 \\ 0 \\ 0 \\ 0 ...
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0 0 votes
1 1 answer
128
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NPTEL GATE CS MOCK TEST 6
According to me both are inferencing each other, please someone suggest whether D is correct or B, if B is correct please provide a valid reason I could not understand wh...
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2 2 votes
1 1 answer
123
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Go classes Linear Algebra weekly quiz 2
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1 1 vote
1 1 answer
192
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GATE CS&DA LA Practice Problem
Let $\mathbf{u}$ and $\mathbf{v}$ be two mutually orthogonal unit vectors in $\mathbb{R}^n$, where $n \ge 3$. A matrix $\mathbf{A}$ is defined using outer products as:$$\...
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2 2 votes
1 1 answer
270
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GATE DA LA Pratice Question
Let $A= [\mathbf{c}_1\ \mathbf{c}_2\ \mathbf{c}_3\ \mathbf{c}_4]$ be a $3 \times 4$ real matrix. The complete solution of$A\mathbf{x} = \begin{bmatrix} 2 \\ -1 \\ 3 \end{...
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127
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subspace and dimension
Let $V$ be a subspace of $\mathbb{R}^{10}$. Suppose $A$ is a $10 \times 10$ matrix with real entries. Let $A^k(V) = \{A^k\mathbf{x} : \mathbf{x} \in V\}$ for $k \ge 1$ an...
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1 1 vote
1 1 answer
171
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​GATE - 2007 EE | LINEAR ALGEBRA QUESTION
​GATE - 2007 EE | LINEAR ALGEBRA QUESTION    The solution I found is a bit odd. I have my own approach: first, take x common and then y common. After analyzing it, I can...
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2 2 votes
0 0 answers
117
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Go classes Linear Algebra Module 1 6D lecture
I recently tried to build an intuition for why the number of linearly independent rows must equal the number of linearly independent columns after watching the Lecture re...
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4 4 answers
570
570 views
Relation between rank and eigen value.
Let $A$ be a 5 x 5 matrix and $\lambda_1$ be one of the eigen value of $A$ such that $\text{rank}(A-\lambda_1I) = 2$, then geometric multiplicity of $\lambda_1$ is ______...
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5 5 votes
4 4 answers
429
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rank-of-matrix
If matrix A has full rank, then what are the valid conclusions from the followingA is a full row rank matrixA is a full column rank matrixA is invertibleCan't say
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26 26 votes
4 4 answers
1.9k
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GO Classes DPP | GATE CS | Linear Algebra | Invertibility of a Matrix
For which values of $a$ is the matrix$A = \begin{bmatrix}1 & -1 & 0 \\1 & 0 & -1 \\0 & a & 2\end{bmatrix}$invertible?$a = -2$$a \neq -2$$a = 2$All real $a$
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30 30 votes
3 3 answers
1.2k
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GO Classes DPP | GATE CS | Linear Algebra | Determinant
Find the value of$\begin{vmatrix}0 & 0 & 0 & 0 & 0 & 6 \\0 & 0 & 0 & 0 & 5 & 6 \\0 & 0 & 0 & 4 & 5 & 6 \\0 & 0 & 3 & 4 & 5 & 6 \\0 & 2 & 3 & 4 & 5 & 6 \\1 & 2 & 3 & 4 & 5...
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30 30 votes
6 6 answers
1.1k
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GO Classes DPP | GATE CS | Linear Algebra | System of Linear Equations
Which of the following represents the complete solution set of the given system?$$\begin{bmatrix}1 & 0 & 0 & 2 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & -1\end{bmatrix}\begin{bmatrix...
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17 17 votes
1 1 answer
810
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GO Classes DPP | GATE CS | Linear Algebra | Determinant
Consider the following statements:If $\text{det}(A) \neq 0 $ then $Ax = b$ has a unique solution. If $Ax = b$ has solutions $u_1 = \begin{pmatrix} 2 \\ 2 \\ 2 \end{pmatri...
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19 19 votes
1 1 answer
664
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GO Classes DPP | GATE CS | Linear Algebra | Determinant | Symmetric Matrix
Consider the following statements:If $A^{-1} = A^{T}$ then $\text{det} (A^{-1}) = ±1$.If $A$ is any $n \times n$ matrix then $(A + A^T)$ is symmetric. Only statement $\te...
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16 16 votes
1 1 answer
685
685 views
GO Classes DPP | GATE CS | Linear Algebra | Matrix Algebra
Consider three non-zero matrices $A, ~B$ and $C$ such that $ABB^T = CBB^T$ where $B^T$ is the transpose of $B$. Which of the following statements is necessarily true?$r(A...
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14 14 votes
1 1 answer
546
546 views
GO Classes DPP | GATE CS | Linear Algebra | Eigenvalues of Matrix Products
Consider non-zero matrices $A\in M_{m\times n}$, $B\in M_{n\times p}$, and $C\in M_{p\times m}$. Then $ABC$, $BCA$, and $CAB$ are all square matrices. Which of the follow...
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16 16 votes
2 2 answers
680
680 views
GO Classes DPP | GATE CS | Linear Algebra | Matrix Algebra
Let $$ A=\left[\begin{array}{lll} a & 1 & 1 \\ b & a & 1 \\ 1 & 1 & 1 \end{array}\right] . $$ The number of elements in the set $$ \left\{(a, b) \in \mathbb{Z}^{2}: 0 \le...
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9 9 votes
1 1 answer
514
514 views
GO Classes DPP | GATE CS | Linear Algebra | Eigen Vectors
Suppose that a $4 \times 4$ matrix $A$ has eigenvalue $3$. If$A - 3I = \begin{pmatrix} 1 & -2 & 0 & 4 \\ 0 & 0 & 1 & -3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix},$t...
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