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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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Recent questions in Linear Algebra

8 votes
3 answers
721
GATE CSE 1988 | Question: 16i
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangular, and $P$ ... $L, U,$ and $P$ using Gaussian elimination with partial pivoting.
Assume that the matrix $A$ given below, has factorization of the form $LU=PA$, where $L$ is lower-triangular with all diagonal elements equal to $1, U$ is upper-triangula...
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1 votes
2 answers
723
MadeEasy Test Series: Linear Algebra - Eigen Value
can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.
can we use some identity to find value of ab+by+ya???without finding its eigen values and then multiplying..earlier i have read it somewhere but i forget it.
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0 votes
0 answers
724
Gate 2006
Qus 1 Qus 2
Qus 1Qus 2
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2 votes
1 answer
725
Gate 2014
Qus 1 Qus2
Qus 1Qus2
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2 votes
1 answer
726
matrix
If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?
If A3x3 is a matrix with |A| = 2. What is the determinant of Adj (Adj (Adj A))?
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0 votes
1 answer
728
Madeeasy workbook
Correct option
Correct option
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0 votes
1 answer
729
gate previous
$\begin{bmatrix}2 &1 & -4\\ 4 & 3 & -12\\ 1 & 2 & -8 \end{bmatrix}\cdot \begin{bmatrix} x\\ y\\ z \end{bmatrix}= \begin{bmatrix} \alpha \\5 \\ 7 \end{bmatrix}$ For how many values of $\alpha$ , this system has infinite solutions ?
$\begin{bmatrix}2 &1 & -4\\ 4 & 3 & -12\\ 1 & 2 & -8 \end{bmatrix}\cdot \begin{bmatrix} x\\ y\\ z \end{bmatrix}= \begin{bmatrix} \alpha \\5 \\ 7 \end{bmatrix}$For how man...
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0 votes
1 answer
730
The value of Z+1/225 = _
A = 2000 B = A – 999 C = A + B – 998 D = A + B + C – 997 . . . Z= A + B + C … + X – 975 The value of Z+1/225 = _______ 501 901 801 2048
A = 2000B = A – 999C = A + B – 998D = A + B + C – 997... Z= A + B + C … + X – 975The value of Z+1/225 = _______ 501 901 801 2048
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0 votes
1 answer
732
Eigen Vector
The number of linearly independent eigen vector of matrix A(3$\times$3) given as following a11=a22=2, a12=1, a13=a21=a23=a31=a32=0, a33=3
The number of linearly independent eigen vector of matrix A(3$\times$3) given as following a11=a22=2, a12=1, a13=a21=a23=a31=a32=0, a33=3
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0 votes
1 answer
733
linear algebra
what is linearly independent eigen vector ? is it a set of vectors ? or we can say a eigen vector is linearly independent or dependent?
what is linearly independent eigen vector ? is it a set of vectors ? or we can say a eigen vector is linearly independent or dependent?
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0 votes
1 answer
734
Linear Dependent
I am getting independent but answer is given as dependent. Can some one tell me what worng with my approach
I am getting independent but answer is given as dependent. Can some one tell me what worng with my approach
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1 votes
0 answers
735
Series expansion
If m and n are whole numbers and $m^{n} = 125$ then the value of $(m-5)^{n+1}=?$
If m and n are whole numbers and $m^{n} = 125$ then the value of $(m-5)^{n+1}=?$
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3 votes
1 answer
736
Matrix
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18 votes
3 answers
737
GATE CSE 1987 | Question: 1-xxiii
A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above
A square matrix is singular whenever The rows are linearly independentThe columns are linearly independentThe row are linearly dependentNone of the above
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12 votes
4 answers
738
GATE CSE 1987 | Question: 1-xxi
If $a, b,$ and $c$ are constants, which of the following is a linear inequality? $ax+bcy=0$ $ax^{2}+cy^{2}=21$ $abx+a^{2}y \geq 15$ $xy+ax \geq 20$
If $a, b,$ and $c$ are constants, which of the following is a linear inequality?$ax+bcy=0$$ax^{2}+cy^{2}=21$$abx+a^{2}y \geq 15$$xy+ax \geq 20$
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1 votes
1 answer
740
Characteristic Equation of MAtrix
Conventional way to find the characteristic equation is tough here...Any efficient way anyone?
Conventional way to find the characteristic equation is tough here...Any efficient way anyone?
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