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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

5 votes
1 answer
541
Matrix
If $A=\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$ then$AAA^{T}=3I$ $I$ is a $3\times 3$ identity matrix $\left (a,b \right )$ can be ____________
If$A=\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$then$AAA^{T}=3I$$I$ is a $3\times 3$ identity matrix$\left (a,b \right )$ can be ____________
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0 votes
0 answers
542
test series
A 3 X 3 matrix M has two linearly independent eigen vectors corresponding to eign value 4 and one eigen vector corresponding to eign value 1. What is the value of determinant of M?
A 3 X 3 matrix M has two linearly independent eigen vectors corresponding to eign value 4 and one eigen vector corresponding to eign value 1. What is the value of determi...
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3 votes
2 answers
543
Recurrance Relations
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3 votes
0 answers
545
rank of matrix
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix.(A) Always true(B) ...
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1 votes
0 answers
546
Can one tell what it ask for finding ?
In an M×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
In an M×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, i...
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1 votes
3 answers
547
NUMBER of soutions the equations have?
Consider the following system system of equations x1-2x3=0 x1-x2=0 2x1-2x2=0 No solution Infinite number of solutions Three solution unique solution
Consider the following system system of equationsx1-2x3=0x1-x2=02x1-2x2=0 No solution Infinite number of solutions Three solutionunique solution
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0 votes
1 answer
548
Matrices - LU Decompostion
Is LU Decomposition possible for every matrix ?
Is LU Decomposition possible for every matrix ?
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0 votes
0 answers
550
number of solutions
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0 votes
2 answers
551
Engineering Mathematics - Linear Algebra
If the equations (λ+1)x + 8y = 4λ and λx + (λ+3)y = 3λ-1 have no solution, then the number of values of λ is : (A) one (B) two (C) three (D) more than three
If the equations (λ+1)x + 8y = 4λ and λx + (λ+3)y = 3λ-1 have no solution, then the number of values of λ is :(A) one (B) two (C) three (D) more than three
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0 votes
0 answers
552
System of equations
In this, I could draw the conclusion from the question that there would be no or infinitely many solutions but could not be able to reach how infinitely many solutions is the answer.
In this, I could draw the conclusion from the question that there would be no or infinitely many solutions but could not be able to reach how infinitely many solutions is...
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0 votes
1 answer
553
Practice Set
The system of equation x + y + z = 1, 2x + 3y + 4z = 1 and 4x + 5y + 6z = 2 has (a) unique solution (b) infinite solution (c) no solution (d) none of these
The system of equation x + y + z = 1, 2x + 3y + 4z = 1 and 4x + 5y + 6z = 2 has(a) unique solution (b) infinite solution(c) no solution (d) none of these
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5 votes
1 answer
554
Gilbert Strang
How many n*n (0,1) matrix are invertable ? PS: original question in book is for 2*2
How many n*n (0,1) matrix are invertable ?PS: original question in book is for 2*2
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5 votes
2 answers
555
Matrices
Consider the following matrix $A=\begin{bmatrix} a&a^{2} &a^{3}-1 \\ b& b^{2} &b^{3}-1 \\ c& c^{2}&c^{3}-1 \end{bmatrix}$ if $|A|=0$, then the value of $abc$ is _______________
Consider the following matrix$A=\begin{bmatrix} a&a^{2} &a^{3}-1 \\ b& b^{2} &b^{3}-1 \\ c& c^{2}&c^{3}-1 \end{bmatrix}$if $|A|=0$, then the value of $abc$ is ___________...
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2 votes
0 answers
556
Solution of linear equations
The number of linearly independent solutions of 'm' homogeneous linear equations in 'n' variables ..AX=0 is (n-r) where r is the rank of a matrix..could somebody explain me by giving proper reasoning as how?...Thanks
The number of linearly independent solutions of 'm' homogeneous linear equations in 'n' variables ..AX=0 is (n-r) where r is the rank of a matrix..could somebody explain ...
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0 votes
0 answers
557
Matrix doubt
A= 1 2 2 2 1 -2 a 2 b And AAA^T = 3l I is 3*3 identity matrix a ,b can be.... A) 2,-1 B) -2,1 C) -2,-1 D) none
A= 12221-2a2bAnd AAA^T = 3lI is 3*3 identity matrixa ,b can be....A) 2,-1B) -2,1C) -2,-1D) none
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0 votes
1 answer
559
Problem in linear algebra
How many solutions does the following system of linear equations have? X+5y = -1 x-y = 2 x+3y = 3 A. infinitely many B. two distinct solutions C. unique D. no solution
How many solutions does the following system of linear equations have?X+5y = -1x-y = 2x+3y = 3 A. infinitely manyB. two distinct solutionsC. uniqueD. no solution
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0 votes
1 answer
560
Matrix doubt
If matrix A = 1 2 -1 -1 1 2 2 -1 1 Then find det(adj(adj A)) is a) 14^4 b)14^6 c)14^9 d)14^2
If matrix A = 12-1-1122-11Then find det(adj(adj A)) isa) 14^4b)14^6c)14^9d)14^2
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