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Recent questions tagged linear-algebra
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61
GATE 2023 | MATHS | Question 59
Let \(A\) be a \(3 \times 3\) real matrix with \(\text{det}(A + iI) = 0\), where \(i = \sqrt{-1}\) and \(I\) is the \(3 \times 3\) identity matrix. If \(\text{det}(A) = 3\), then the trace of \(A^2\) is \(\underline{\hspace{1cm}}\).
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
91
views
linear-algebra
0
votes
1
answer
62
GATE 2023 | Maths | Problems for DA Paper
Consider the linear system \(Mx = b\), where \[ M = \begin{bmatrix} 2 & -1 \\ -4 & 3 \end{bmatrix} \] and \[ b = \begin{bmatrix} -2 \\ 5 \end{bmatrix} \]. Suppose \(M = LU\), where \(L\) and \(U\) are lower triangular and upper ... (A) both π and π are TRUE (B) π is FALSE and π is TRUE (C) π is TRUE and π is FALSE (D) both π and π are FALSE
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
88
views
linear-algebra
0
votes
1
answer
63
GATE 2023 | Maths | Linear Alegbra
Let \( M = \begin{bmatrix} 3 & -1 & -2 \\ 0 & 2 & 4 \\ 0 & 0 & 1 \end{bmatrix} \) and \( I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \). If \( 6M^{-1} = M^2 - 6M + \alpha I \) for some \( \alpha \in \mathbb{R} \), then the value of \( \alpha \) is equal to \(\underline{\hspace{1cm}}\).
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
80
views
linear-algebra
0
votes
0
answers
64
GATE 2023 | Maths | Practice Problem for DA Paper
Let \( T: \mathbb{R}^4 \rightarrow \mathbb{R}^4 \) be a linear transformation, and the null space of \( T \) be the subspace of \( \mathbb{R}^4 \) given by \[ \{ (x_1, x_2, x_3, x_4) \in \mathbb{R}^4 : 4x_1 + 3x_2 + 2x_3 + x_4 = 0 \}. \] If \( \text{Rank}(T - 3I) = ... \( x(x - 3) \) (B) \( x(x - 3)^3 \) (C) \( x^3(x - 3) \) (D) \( x^2(x - 3)^2 \)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
61
views
linear-algebra
0
votes
0
answers
65
GATE 2023 | MATHS | Practice Problem for DA Paper
Let \(M = \begin{bmatrix} 4 & -3 \\ 1 & 0 \end{bmatrix}\). Consider the following statements: \(P:\ M^8 + M^{12}\) is diagonalizable. \(Q:\ M^7 + M^9\) is diagonalizable. Which of the following statements is correct? (A) $π$ is $TRUE$ ... $π$ is $FALSE$ and $π$ is $TRUE$ (C) Both $π$ and $π$ are $FALSE$ (D) Both $π$ and $π$ are $TRUE$
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
92
views
linear-algebra
0
votes
0
answers
66
GATE DA - 2024 | Linear Algebra
Let $π΄$ be an $π π$ real matrix. Consider the following statements. $(I)$ If $π΄$ is symmetric, then there exists $π β₯ 0$ such that $π΄ + ππΌ_π$ is symmetric and positive definite, where $πΌ_π$ is the $π π$ identity matrix $(II)$ If $π΄$ is symmetric and ... above statements is/are true? (A) Only (I) (B) Only (II) (C) Both (I) and (II) (D) Neither (I) nor (II)
rajveer43
asked
in
Linear Algebra
Jan 10
by
rajveer43
86
views
linear-algebra
0
votes
0
answers
67
#self doubt
Can someone please explain why no of lineary independent solutions are n-r .β¦ My confusion is if in 3*3 Matrix rank is 2 means 2 lineary independent rows right? How solution is getting calculated as 3-2=1?
Dknights
asked
in
Linear Algebra
Jan 10
by
Dknights
50
views
linear-algebra
engineering-mathematics
0
votes
2
answers
68
GATE 2022 | Statistics | Question 47
Let π΄ be any 3 Γ 3 symmetric matrix with eigenvalues 1, 2 and 3. Let π΅ be any 3 Γ 3 matrix with real eigenvalues such that $π΄π΅ + π΅^Tπ΄ = 3π°$, where π° is the 3 Γ 3 identity matrix. Then which of the following cannot be eigenvalue(s) of the matrix π΅ ? (A) 1/4 (B) 3/4 (C) 1/2 (D) 7/4
rajveer43
asked
in
Linear Algebra
Jan 9
by
rajveer43
143
views
linear-algebra
0
votes
0
answers
69
GATE 2022 Stat | Question 16 | Linear Algebra
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
35
views
linear-algebra
1
vote
0
answers
70
GATE 2022 | Linear Algebra | Question 11
Let π΄ be a 2 Γ 2 real matrix such that $(π° + π΄)^-1 = π° β πΌπ΄$, where πΌ is a non-zero real number and π° is the 2 Γ 2 identity matrix. If the trace of the matrix π΄ is 3, then the value of πΌ is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4
rajveer43
asked
in
Mathematical Logic
Jan 9
by
rajveer43
73
views
linear-algebra
0
votes
0
answers
71
Linear Algebra, Eigen Vales & Eigen Vectors
$If \ A = \begin{pmatrix} 1&1 \\ 1&0 \end{pmatrix},\ \alpha M_1+\beta M_2+\gamma M_3,\ where \ M_1 = L_{2x2},\ M_2 = \begin{pmatrix} 0&1 \\ 1&1 \end{pmatrix}\ and \ M_3 = \begin{pmatrix} 1&1 \\ 1&1 \end{pmatrix} \ then \ -$ ... $\alpha = 1,\ \beta = -1,\ \gamma = 2$ D. $\alpha = -1,\ \beta = 1,\ \gamma = 2$
Debargha Mitra Roy
asked
in
Linear Algebra
Jan 8
by
Debargha Mitra Roy
94
views
engineering-mathematics
linear-algebra
eigen-value
matrix
0
votes
1
answer
72
#self doubt
I found this statement in math blog.....can anyone please help on this⦠For a upper triangular Matrix I tried to derive with Eigen values as 1,2,0,0,0 for 5*5 but I am not getting rank as 2 for this Matrix.
Dknights
asked
in
Linear Algebra
Jan 7
by
Dknights
91
views
engineering-mathematics
linear-algebra
0
votes
0
answers
73
Find the basic feasible solutions
Find the basic feasible solutions of the system of equations :- $x_1+x_2+x_3=8,$ $3x_1+2x_2=18,$ $x_1,x_2,x_3β₯ 0$
Debargha Mitra Roy
asked
in
Linear Algebra
Dec 11, 2023
by
Debargha Mitra Roy
138
views
linear-algebra
matrix
0
votes
0
answers
74
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
Gaurav Kadyan
asked
in
Linear Algebra
Nov 10, 2023
by
Gaurav Kadyan
198
views
usergate2017
usermod
engineering-mathematics
linear-algebra
0
votes
3
answers
75
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 $12$ $10$ $8$ $6$
admin
asked
in
Linear Algebra
Oct 22, 2023
by
admin
1.3k
views
gateda-sample-paper-2024
linear-algebra
eigen-value
0
votes
0
answers
76
Made Easy Test Series 2024
please anyone explain this question .?
Ray Tomlinson
asked
in
Calculus
Oct 12, 2023
by
Ray Tomlinson
341
views
made-easy-test-series
made-easy-booklet
calculus
linear-algebra
made-easy-test-series-2024
0
votes
1
answer
77
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
akshay_123
asked
in
Linear Algebra
Sep 8, 2023
by
akshay_123
366
views
engineering-mathematics
linear-algebra
0
votes
1
answer
78
practice book gate
the eigen values of the matrix are (a) (a+1), 0 (b) a, 0 (c) (a-1), 0 (d) 0, 0
akshay_123
asked
in
Linear Algebra
Sep 8, 2023
by
akshay_123
272
views
engineering-mathematics
linear-algebra
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