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Recent questions tagged linear-algebra

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122
GATE 2022 | Linear Algebra | Question 11
Let 𝑴 be a 2 Γ— 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 βˆ’ 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 Γ— 2 identity matrix. If the trace of the matrix 𝑴 is 3, then the value of 𝛼 is (A) 3/4 (B) 1/3 (C) 1/2 (D) 1/4
Let 𝑴 be a 2 Γ— 2 real matrix such that $(𝑰 + 𝑴)^-1 = 𝑰 βˆ’ 𝛼𝑴$, where 𝛼 is a non-zero real number and 𝑰 is the 2 Γ— 2 identity matrix. If the tra...
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125
#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.
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 n...
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0 votes
0 answers
126
Find the basic feasible solutions
Find the basic feasible solutions of the system of equations :- $x_1+x_2+x_3=8,$ $3x_1+2x_2=18,$ $x_1,x_2,x_3β‰₯ 0$
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$
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127
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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0 votes
3 answers
128
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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130
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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131
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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