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Syllabus: Matrices, determinants, System of linear equations, Eigenvalues and eigenvectors, LU decomposition.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 1 &0&1&0&1&1&1&1&1&2&0&0.9&2
\\\hline\textbf{2 Marks Count} & 2 &1&1&1&1&1&2&1&0&0&0&1&2
\\\hline\textbf{Total Marks} & 5 &2&3&2&3&3&5&3&1&2&\bf{1}&\bf{2.9}&\bf{5}\\\hline
\end{array}}}$$

Hot questions in Linear Algebra

0 votes
0 answers
94
Can someone please explain why no of lineary independent solutions are n-r .…My confusion is if in 3*3 Matrix rank is 2 means 2 lineary independent rows right? How sol...
0 votes
0 answers
96
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$
0 votes
0 answers
97
rank of a matrix = number of non-zero eigenvalues always?
0 votes
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99
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...
0 votes
1 answer
101
the eigen values of the matrix are (a) (a+1), 0(b) a, 0(c) (a-1), 0(d) 0, 0
0 votes
1 answer
102
The number of linearly independent solutions of the system of equationsis equal toA- 1B- 2C-3D- 0
17 votes
2 answers
103
Consider Three matrices $A, B$ and $C$ such that -$$\underbrace{\left(\begin{array}{lllll}1 & 2 & 4 & 2 & 5 \\& 2 & 3 & 5 & 6 \\& & 3 & 4 & 3 \\& & & 4 & 3 \\& & & 5\end{...
26 votes
3 answers
105
Let $A$ and $B$ be real symmetric matrices of size $n \times n$. Then which one of the following is true?$AA'=I$$A=A^{-1}$$AB=BA$$(AB)'=BA$
3 votes
3 answers
106
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ hasThe trivial solution $X=0$.One independent solution.Two independent solution.Three independent solution.
22 votes
3 answers
107
Consider the following set of equations$x+2y=5$$4x+8y=12$$3x+6y+3z=15$This sethas unique solutionhas no solutionhas finite number of solutionshas infinite number of solut...
0 votes
3 answers
109
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...
26 votes
7 answers
110
The determinant of the matrix $$\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$$$4$$0$$15$$20$