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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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Most viewed questions in Linear Algebra

0 votes
1 answer
331
ISI2015-DCG-32
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is $\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \end{Bmatrix}$ ... None of these
The set of vectors constituting an orthogonal basis in $\mathbb{R} ^3$ is$\begin{Bmatrix} \begin{pmatrix} 1 \\ -1 \\ 0 \end{pmatrix}, & \begin{pmatrix} 1 \\ 1 \\ 0 \end{p...
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0 answers
333
Gate cs 2007
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5 votes
2 answers
334
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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0 votes
1 answer
335
[Gate IN 2016- Set A] Linear algebra,Eigen values
If we solve this we will get total 4 eigen vectors,but as we know that this is of 2 degree matrix so only 2 will exist.So can i say that from these four pairs by using nay 2 ,i can derive the other?If yes,then how?
If we solve this we will get total 4 eigen vectors,but as we know that this is of 2 degree matrix so only 2 will exist.So can i say that from these four pairs by using na...
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0 votes
2 answers
336
Matrices
If AB=BA then which of following are true? 1)(A+B)(A-B)=A^2-B^2 2)(AB)^n=A^n B^n 3)AB^n=B^n A 4)A=I or B=I
If AB=BA then which of following are true?1)(A+B)(A-B)=A^2-B^22)(AB)^n=A^n B^n3)AB^n=B^n A4)A=I or B=I
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3 votes
3 answers
337
NIELIT 2016 DEC Scientist B (IT) - Section B: 26
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+​ \sqrt-1)$ and $3$. The determinant of $P$ is ________. $0$ $1$ $15$ $-1$
Two eigenvalues of a $3\times3$ real matrix $P$ are $(2+​ \sqrt-1)$ and $3$. The determinant of $P$ is ________.$0$$1$$15$$-1$
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4 votes
1 answer
340
GATE Overflow | Mock GATE | Test 1 | Question: 52
$\begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$ For the above given matrix $A,$ $A^3 -7A^2 +10A = $ $5I+A$ $5I-A$ $A-5I$ $6I$
$\begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$For the above given matrix $A,$$A^3 -7A^2 +10A = $$5I+A$$5I-A$$A-5I$$6I$
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2 votes
1 answer
342
ISI2019-MMA-14
If the system of equations $\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$ with $a,b,c \neq 1$ has a non trivial solutions, the value of $\frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c}$ is $1$ $-1$ $3$ $-3$
If the system of equations$\begin{array} \\ax +y+z= 0 \\ x+by +z = 0 \\ x+y + cz = 0 \end{array}$with $a,b,c \neq 1$ has a non trivial solutions, the value of $$\frac{1}{...
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1 answer
344
use of calculator
Can we use calculator provided in exam to find out determinant?
Can we use calculator provided in exam to find out determinant?
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0 votes
1 answer
346
is there any short cut to find the determinant of the matrix
1 0 0 0 0 2 0 1 0 0 2 0 0 0 1 2 0 0 0 0 2 1 0 0 0 2 0 0 1 0 2 0 0 0 0 1
1 0 0 0 0 20 1 0 0 2 00 0 1 2 0 00 0 2 1 0 00 2 0 0 1 02 0 0 0 0 1
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0 votes
1 answer
348
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
349
Matrices - LU Decompostion
Is LU Decomposition possible for every matrix ?
Is LU Decomposition possible for every matrix ?
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0 votes
1 answer
350
Math Linear Algebra
If A and B are real symmetric matrices of size n*n. Then, which one of the following is true? a) AA^t = I b) A = A^-1 c) AB =BA d) (AB)^t = BA
If A and B are real symmetric matrices of size n*n. Then, which one of the following is true?a) AA^t = Ib) A = A^-1c) AB =BAd) (AB)^t = BA
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