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Recent questions tagged linear-algebra

1 votes
2 answers
601
linear algebra
How many different entries can a 4 * 4 skew-symmetric matrix have? An n* n skew-symmetric matrix? What if it is symmetric matrix ?
How many different entries can a 4 * 4 skew-symmetric matrix have? An n* n skew-symmetric matrix? What if it is symmetric matrix ?
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1 votes
1 answer
602
Linear algebra Determinant
True/False A matrix is singular iff any row/column is constant multiple of any other row/column?
True/FalseA matrix is singular iff any row/column is constant multiple of any other row/column?
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2 votes
1 answer
603
Calculate Eigen Vector And Eigen Value
This matrix is singular with rank one. Find three $λ$’s and three eigenvectors. $\begin{bmatrix}1\\2 \\1 \end{bmatrix}$ $\begin{bmatrix}2&1 &2 \end{bmatrix}$ = $\begin{bmatrix}2 & 1 &2\\4 & 2 & 4\\2 & 1 &2\end{bmatrix}$
This matrix is singular with rank one. Find three $λ$’s and three eigenvectors.$\begin{bmatrix}1\\2 \\1 \end{bmatrix}$ $\begin{bmatrix}2&1 &2 \end{bmatrix}$ = $\begin...
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3 votes
1 answer
604
Find the last row of the Matrix
For the first one I have got -28 and 11 as the answer but for the matrix C I am not able to get the value of element c32. c31 = c33 = 6.
For the first one I have got -28 and 11 as the answer but for the matrix C I am not able to get the value of element c32.c31 = c33 = 6.
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2 votes
1 answer
605
State true/ false (with reason) For Linear Algebra
Q1> Is it possible to have no Eigen vector corresponding to an Eigen value. Q2> Rank of a matrix is equal to the number of non-zero Eigen values that matrix has. {Explain with reason and counter example.}
Q1 Is it possible to have no Eigen vector corresponding to an Eigen value.Q2 Rank of a matrix is equal to the number of non-zero Eigen values that matrix has.{Explain wit...
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1 votes
1 answer
607
Linear Algebra by Gilbert strang, 4th edition, 5.1.13
If B has eigenvalues 1, 2, 3, C has eigenvalues 4, 5, 6, and D has eigenvalues 7, 8, 9, what are the eigenvalues of the 6 by 6 matrix A =[ B C , 0 D] ?
If B has eigenvalues 1, 2, 3, C has eigenvalues 4, 5, 6, and D has eigenvalues 7, 8,9, what are the eigenvalues of the 6 by 6 matrix A =[ B C , 0 D] ?
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3 votes
1 answer
608
Gate EE 2014 Eigen values
A system matrix is given as follows. The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
A system matrix is given as follows.The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
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0 votes
1 answer
609
[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
0 answers
610
[Linear Algebra]
What is the effect of elementary operations on eigen vectors ? I know eigen values are not preserved with elementary operations,so as eigen vectors are generated by eigen values so they should change,But i am not sure.
What is the effect of elementary operations on eigen vectors ?I know eigen values are not preserved with elementary operations,so as eigen vectors are generated by eigen ...
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0 votes
0 answers
612
[Linear algebra]Determinant of matrix
True /false If any row/column is constant is constant multiple of any other row/column then determinant is zero. Whether the converse of this statement is true or false?
True /falseIf any row/column is constant is constant multiple of any other row/column then determinant is zero.Whether the converse of this statement is true or false?
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0 votes
1 answer
613
Linear Algebra-Determinant
Suppose det(A)=4 then how we could find the det(a^4) ? A is a square matrix of order 4X4 .
Suppose det(A)=4 then how we could find the det(a^4) ?A is a square matrix of order 4X4 .
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4 votes
1 answer
614
Gate ME 2016: Eigen value
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 &k \end{bmatrix}$ are positive is $k > \frac{1}{2}$ $ k > −2$ $ k > 0$ $k< \frac{-1}{2}$
The condition for which the eigenvalues of the matrix $A=\begin{bmatrix} 2 & 1\\ 1 &k \end{bmatrix}$ are positive is$k \frac{1}{2}$$ k −2$$ k 0$$k< \frac{-1}{2}$
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1 votes
1 answer
615
Question on Solving System of Homogenous Linear Equation
While Solving System of Homogenous Linear Equations, why can't r > n i.e. rank of matrix > number of variables/unknown thanks!
While Solving System of Homogenous Linear Equations, why can'tr ni.e.rank of matrix number of variables/unknown thanks!
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1 votes
0 answers
616
Linear algebra
Let A be n*n matrix,$A^{n}$ = $A^{n-1}$ for n>=1 and $A^{0}$=I,Which of following is true? a.$A^{m}$ .$A^{n}$ =$A^{m+n}$ b. $($A^{m}$)^{n}$=$A^{mn}$ c. both a and b c none
Let A be n*n matrix,$A^{n}$ = $A^{n-1}$ for n>=1 and $A^{0}$=I,Which of following is true? a.$A^{m}$ .$A^{n}$ =$A^{m+n}$b. $($A^{m}$)^{n}$=$A^{mn}$$c. both a and bc none
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0 votes
2 answers
621
How to solve this Determinant question
2a1b1 a1b2+a2b1 a1b3+a3b1 a1b2+a2b1 2a2b2 a2b3+a3b1 a1b3+a3b1 a3b2+a2b3 2a3b3 Express this 3x3 determinant as product of 2 determinants and find it's value
2a1b1a1b2+a2b1a1b3+a3b1a1b2+a2b12a2b2a2b3+a3b1a1b3+a3b1a3b2+a2b32a3b3Express this 3x3 determinant as product of 2 determinants and find it's value
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0 votes
2 answers
622
Question regarding symmetric matrix
Is every square matrix a symmetric matrix? Or Is every square DIAGONAL matrix is a symmetric matrix? Please tell which statement is true?
Is every square matrix a symmetric matrix?OrIs every square DIAGONAL matrix is a symmetric matrix?Please tell which statement is true?
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9 votes
2 answers
623
Mathematics: Gate 2016 EE set-2
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are: 1) 1, 1, -1 2) 1, 0.5 + j0.866, 0.5 - j0.866 3) 1, -0.5 + j0.866, -0.5 - j0.866 4) 0, 1, -1
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are:1) 1, 1, -12) 1, 0.5 + j0.866, 0.5 - j0.8663) 1, -0.5 + j0.866, -0.5 - j0.8664) 0, 1, -1
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1 votes
2 answers
627
Test by Bikram | Mock GATE | Test 4 | Question: 1
The sum of the diagonal elements of a $ 2\times 2 $ upper triangular matrix is $-6.$ Then, the maximum possible value of the determinant of the matrix is ________.
The sum of the diagonal elements of a $ 2\times 2 $ upper triangular matrix is $-6.$ Then, the maximum possible value of the determinant of the matrix is ________.
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1 votes
1 answer
628
matrices
Let A be a real $2 \times 2$ matrix.If $5 + 3\iota$ is an eigen value of A, then det(A) (A)equals 4 (B)equals 8 (C)equals 16
Let A be a real $2 \times 2$ matrix.If $5 + 3\iota$ is an eigen value of A, then det(A)(A)equals 4(B)equals 8(C)equals 16
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1 votes
1 answer
629
Matrices
Let $\begin{pmatrix} -1 &2 \\ 0 & -1 \end{pmatrix}$,and $B=A+A^{2}+A^{3}+\dots +A^{50}$, then $B^{2}=I$ $B^{2}=0$ $B^{2}=A$ $B^{2}=B$
Let $\begin{pmatrix} -1 &2 \\ 0 & -1 \end{pmatrix}$,and $B=A+A^{2}+A^{3}+\dots +A^{50}$, then$B^{2}=I$ $B^{2}=0$ $B^{2}=A$ $B^{2}=B$...
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11 votes
3 answers
630
ISRO2017-1
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ is Diagonal matrix $\text{A}$ $0$ $-\text{A}$
If $\text{A}$ is a skew symmetric matrix then $\text{A}^t$ isDiagonal matrix $\text{A}$$0$$-\text{A}$
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