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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

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Highest voted questions in Linear Algebra

2 votes
1 answer
363
system of equations
value of k for which system of equations x+2y+kz=1 2x+ky+8z=3 has no solution 1)0 2)2 3)4 4) 8
value of k for which system of equations x+2y+kz=1 2x+ky+8z=3 has no solution 1)02)23)44) 8
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2 votes
1 answer
365
TIFR-2011-Maths-B-13
Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.
Any non-singular $k \times k$-matrix with real entries can be made singular by changing exactly one entry.
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2 votes
1 answer
366
TIFR-2011-Maths-B-8
If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
If $A$ and $B$ are $3 \times 3$ matrices and $A$ is invertible, then there exists an integer $n$ such that $A + nB$ is invertible.
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2 votes
0 answers
367
TIFR-2011-Maths-A-18
Consider the map $T$ from the vector space of polynomials of degree at most $5$ over the reals to $R \times R$, given by sending a polynomial $P$ to the pair $(P(3), P' (3))$ where $P'$ is the derivative of $P$. Then the dimension of the kernel is $3$.
Consider the map $T$ from the vector space of polynomials of degree at most $5$ over the reals to $R \times R$, given by sending a polynomial $P$ to the pair $(P(3), P' (...
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2 votes
1 answer
368
TIFR-2011-Maths-A-13
$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations, $Ax = b$ has exactly one solution.
$A$ is $3 \times 4$-matrix of rank $3$. Then the system of equations,$Ax = b$has exactly one solution.
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2 votes
1 answer
370
What is the number of linearly independent solutions of a set of vectors taken from identity matrix?
If I have 3 sets of vectors X=(1,0,0) , Y= (0,1,0) and Z=(0,0,1) then these all form a linearly independent set of vectors ,so K(X)+P(Y)+Q(Z) =0 , so we get K=P=Q=0 , but...
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2 votes
1 answer
371
If rank of a matrix is n-1 then how is it that adjoint of matrix is not equal to zero ?
Clearly |A|=0 ,so A*adj A=0 now since A is not null therefore Adj A can be anything , is may or may not be null so how can we say directly that adj A is not equal to 0        
Clearly |A|=0 ,so A*adj A=0 now since A is not null therefore Adj A can be anything , is may or may not be null so how can we say directly that adj A is not equal to 0 �...
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2 votes
1 answer
373
How to prove Rank(AB) <= min(Rank(A),Rank(B)) ?
Given A and B are matrices such that they can be multiplied. How to prove Rank(AB) ≤ min(Rank(A),Rank(B)) ?
Given A and B are matrices such that they can be multiplied.How to prove Rank(AB) ≤ min(Rank(A),Rank(B)) ?
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2 votes
1 answer
374
Diagonal Matrices
If diagonal matrix is commutative with every matrix of same order then it is necessarily 1)scalar matrix 2)unit matrix 3)symmetric matrix 4)zero matrix
If diagonal matrix is commutative with every matrix of same order then it is necessarily1)scalar matrix2)unit matrix3)symmetric matrix4)zero matrix
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1 votes
1 answer
376
GO Classes DA 2025 | Weekly Quiz 6 | Change of Basis & Linear Transformation | Question: 10
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ ... $\left(\begin{array}{lll}2 & 1 & 3 \\ 6 & 3 & 9\end{array}\right)$
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ be a linear transformation such that $T\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right]=\left[\begin{array}{l}2 \\ 6...
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1 votes
1 answer
379
GO Classes CS/DA 2025 | Weekly Quiz 5 | Linear Algebra | Question: 11
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ? $6 \times 7$ $4 \times 5$ $7 \times 6$ $5 \times 4$
The rank and nullity of a matrix $A$ are 4 and 2 , respectively. The nullity of $A^{\top}$ is 3 . What are the dimensions of $A$ ?$6 \times 7$$4 \times 5$$7 \times 6$$5 \...
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