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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

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91
Find the basic feasible solutions
Find the basic feasible solutions of the system of equations :- $x_1+x_2+x_3=8,$ $3x_1+2x_2=18,$ $x_1,x_2,x_3≥ 0$
Find the basic feasible solutions of the system of equations :-$x_1+x_2+x_3=8,$$3x_1+2x_2=18,$$x_1,x_2,x_3≥ 0$
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92
#linear algebra#eigen values
rank of a matrix = number of non-zero eigenvalues always?
rank of a matrix = number of non-zero eigenvalues always?
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93
Pyq
If a square matrix of order 100 has exactly 15 distinct eigen values, the degree of the minimal polynomial is (a) At least 15 (c) Always 15 (b) At most 15 (d) Exactly 100
If a square matrix of order 100 has exactly 15 distinct eigen values, the degree of the minimal polynomial is (a) At least 15 (c) Always 15 (b) At most 15 (d) Exactly 100...
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3 answers
94
GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 17
For matrix $H=\left[\begin{array}{cc}9 & -2 \\ -2 & 6\end{array}\right]$, one of the eigenvalues is $5$. Then, the other eigenvalue is $12$ $10$ $8$ $6$
For matrix $H=\left[\begin{array}{cc}9 & -2 \\ -2 & 6\end{array}\right]$, one of the eigenvalues is $5$. Then, the other eigenvalue is$12$$10$$8$$6$
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95
practice book gate
The number of linearly independent solutions of the system of equations is equal to A- 1 B- 2 C-3 D- 0
The number of linearly independent solutions of the system of equationsis equal toA- 1B- 2C-3D- 0
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1 answer
96
practice book gate
the eigen values of the matrix are (a) (a+1), 0 (b) a, 0 (c) (a-1), 0 (d) 0, 0
the eigen values of the matrix are (a) (a+1), 0(b) a, 0(c) (a-1), 0(d) 0, 0
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3 answers
97
Sachin Mittal Sir's course on GO Classes
It is given that m < n lets consider m = 4 and n = 5. If rank(A) = n, this means no of linearly independent columns in A are 5, but we cannot have 5 linearly independent vectors in R4. Where is the problem ?
It is given that m < nlets consider m = 4 and n = 5.If rank(A) = n, this means no of linearly independent columns in A are 5, but we cannot have 5 linearly independent ve...
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1 answer
98
GO class
sir in this question m should be equal to n without this how rank=n?
sir in this question m should be equal to n without this how rank=n?
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1 answer
99
test series
@sachinmittal1 ​​​​​sir, please verify this table it is for maybe condition.
@sachinmittal1 ​​​​​sir, please verify this table it is for maybe condition.
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1 answer
100
Possible Solutions for a System of Linear Equations
Consider a matrix of dimensions mxn and if rank(A)=n. What can be infer about the possible solutions?
Consider a matrix of dimensions mxn and if rank(A)=n. What can be infer about the possible solutions?
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101
rbr practice questions
Is the product of eigen values of a matrix equal to its determinant true for all the matrices?
Is the product of eigen values of a matrix equal to its determinant true for all the matrices?
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104
#self doubt
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105
#appliedcourse
not getting the answer by 3*3 eigen value formula – (x^3-trace(a)*x^2+sum of minors of a(x)+|a|) eigen values are given as -2,3,6
not getting the answer by 3*3 eigen value formula – (x^3-trace(a)*x^2+sum of minors of a(x)+|a|)eigen values are given as -2,3,6
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