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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&0&2& 1 &0&1&0&0.83&2
\\\hline\textbf{2 Marks Count} &1&1&0& 2 &1&1&0&1&2
\\\hline\textbf{Total Marks} &3&3&2& 5 &2&3&\bf{2}&\bf{3}&\bf{5}\\\hline
\end{array}}}$$

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Recent questions in Linear Algebra

1 votes
0 answers
181
DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where\[M=\left[\begin{array}{cc}4 & 5 \\2 & -5\end{array}\right].\]
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1 votes
1 answer
182
DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$
With no unique solution, solve for $n$ with the following system of equations$$\begin{array}{r}a+b+2 c=3 \\a+2 b+3 c=4 \\a+4 b+n c=6\end{array}$$
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0 votes
1 answer
183
MADEEASY TESTSERIES
To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be made into zero. SO am I wrong or the explanation is wrong?
To justify the OPTION B they gave an example of 2*2 matrix. However we can see that row 2 is linearly dependent on row1. Even though the 2nd row looks non-zero it can be ...
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0 votes
0 answers
184
#LinearAlgebra
Is this correct? ​​​​​
Is this correct?​​​​​
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0 votes
0 answers
186
Matrix
While studying Linear algebra I got 2 perspectives. Which meaning out of these 2 is more accurate?
While studying Linear algebra I got 2 perspectives. Which meaning out of these 2 is more accurate?
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0 votes
2 answers
187
Engineering mathematics
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???
If A is a non-zero column matrix of order n×1 and B is a non-zero row matrix of order 1×n then rank of AB equals ? Rank(ab) can be zero???
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3 votes
3 answers
188
Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ hasThe trivial solution $X=0$.One independent solution.Two independent solution.Three independent solution.
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1 votes
0 answers
189
Self doubt.
If A, B & C are matrices & AB=AC then B=C? as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to say B=C is (always not equal) or (may or may not be equal) or (simply not equal)?
If A, B & C are matrices & AB=AC then B=C?as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to say B=C is ...
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0 votes
0 answers
190
Eigen Value Of A Matrix
For given Matrix: [ 1 2 3 1 5 1 3 1 1 ] Why does the sum of the eigen values of above matrix is the sum of diagonal elements of that matrix?
For given Matrix:[ 1 2 3 1 5 1 3 1 1 ]Why does the sum of the eigen values of above matrix is the sum of diagonal elements of that matrix?
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1 votes
0 answers
191
TIFR CSE 2022 | Part B | Question: 15
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$ ... $\left(a_0, a_1, \ldots, a_d\right) \in S$, the function $ x \mapsto \sum_{i=0}^d a_i x^i $ has a local optimum at $\alpha$
Let $\mathbb{R}$ denote the set of real numbers. Let $d \geq 4$ and $\alpha \in \mathbb{R}$. Let$$ S=\left\{\left(a_0, a_1, \ldots, a_d\right) \in \mathbb{R}^{d+1}: \sum_...
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1 votes
1 answer
199
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|?
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .
Eigen Values of an orthogonal matrix will always be +1 and the modulus will also be always |1|? I have a doubt on this point .
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