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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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Hot questions in Linear Algebra

1 votes
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241
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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0 votes
1 answer
242
Testbook Test Series
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1 answer
243
NPTEL Assignment Question
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35 votes
4 answers
245
GATE CSE 2004 | Question: 76
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row ...
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246
#LinearAlgebra
Is this correct? ​​​​​
Is this correct?​​​​​
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12 votes
2 answers
248
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 35
If $P$ and $Q$ are matrices of same order and $PQ=P$, $QP = Q$, then the expression $(P^5 + Q^5)(P + Q)^5$ evaluates to be $(P + Q)$ $8(P + Q)(1 + 3PQ)$ $16(P +Q)$ $32(P+Q)$
If $P$ and $Q$ are matrices of same order and $PQ=P$, $QP = Q$, then the expression $(P^5 + Q^5)(P + Q)^5$ evaluates to be$(P + Q)$$8(P + Q)(1 + 3PQ)$$16(P +Q)$$32(P+Q)$
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4 votes
2 answers
249
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix But how to calculate value of x when nullity is already given(1 in this case)
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)
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0 votes
0 answers
253
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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2 votes
1 answer
255
NIELIT 2018-27
The following vectors $(1, 9, 9, 8), (2, 0, 0, 8), (2, 0, 0, 3)$ are Linearly dependent Linearly independent Constant None of these
The following vectors $(1, 9, 9, 8), (2, 0, 0, 8), (2, 0, 0, 3)$ areLinearly dependentLinearly independentConstantNone of these
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11 votes
2 answers
256
ISRO2009-60
If two adjacent rows of a determinant are interchanged, the value of the determinant becomes zero remains unaltered becomes infinitive becomes negative of its original value
If two adjacent rows of a determinant are interchanged, the value of the determinantbecomes zeroremains unalteredbecomes infinitivebecomes negative of its original value
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1 votes
0 answers
257
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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1 votes
0 answers
259
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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0 votes
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260
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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