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Recent questions tagged matrix
1
vote
2
answers
151
ISI2019-MMA-15
The rank of the matrix $\begin{bmatrix} 0 &1 &t \\ 2& t & -1\\ 2& 2 & 0 \end{bmatrix}$ equals $3$ for any real number $t$ $2$ for any real number $t$ $2$ or $3$ depending on the value of $t$ $1,2$ or $3$ depending on the value of $t$
Sayan Bose
asked
in
Linear Algebra
May 6, 2019
by
Sayan Bose
1.4k
views
isi2019-mma
linear-algebra
engineering-mathematics
matrix
0
votes
0
answers
152
CSIR UGC NET
Let $A$ be a $3 \times 3$ real matrix. Suppose 1 and -1 are two of the three Eigen values of $A$ and 18 is one of the Eigen values of $A^2+3 A$. Then Both $A$ and $A^2+3 A$ are invertible $A^2+3 A$ is invertible but $A$ is not invertible $A$ is invertible but $A^2+3 A$ is not invertible Both $\mathrm{A}$ and $A^2+3 A$ are not invertible.
Hirak
asked
in
Linear Algebra
Apr 28, 2019
by
Hirak
560
views
linear-algebra
eigen-value
matrix
4
votes
2
answers
153
Nullity of matrix
Nullity of a matrix = Total number columns – Rank of that matrix But how to calculate value of x when nullity is already given(1 in this case)
Nandkishor3939
asked
in
Linear Algebra
Jan 24, 2019
by
Nandkishor3939
3.3k
views
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
0
votes
1
answer
154
Simple Determinant
how to prove determinant 1 and 2 are same by some row-column manipulation ,please Help??
BHASHKAR
asked
in
Linear Algebra
Jan 19, 2019
by
BHASHKAR
303
views
linear-algebra
engineering-mathematics
matrix
0
votes
2
answers
155
Made Easy Workbook
Let A be a 3*3 matrix whose characteristics roots are 3,2,-1. If $B=A^2-A$ then |B|=? a)24 b)-2 c)12 d)-12 Please explain in detail.
Reshu $ingh
asked
in
Linear Algebra
Jan 19, 2019
by
Reshu $ingh
3.2k
views
linear-algebra
matrix
eigen-value
4
votes
2
answers
156
#set theory #groups
Consider the set H of all 3 × 3 matrices of the type: $\begin{bmatrix} a&f&e\\ 0&b&d\\ 0&0&c\\ \end{bmatrix}$ where a, b, c, d, e and f are real numbers and $abc ≠ 0$. Under the matrix multiplication operation, the set H is: (a) a group (b) a monoid but not a group (c) a semigroup but not a monoid (d) neither a group nor a semigroup
Kunal Kadian
asked
in
Set Theory & Algebra
Jan 5, 2019
by
Kunal Kadian
575
views
set-theory&algebra
group-theory
matrix
0
votes
0
answers
157
Determinant
True and false IF A is 5*5 matrix then det(4$A^{3}$)=$4^{5}det(A^{3}))$ det($(4A)^{3}$)=$det(4^{3}A^{3}))$ i think both are true ??
Gurdeep Saini
asked
in
Mathematical Logic
Jan 4, 2019
by
Gurdeep Saini
443
views
engineering-mathematics
matrix
easy
0
votes
0
answers
158
GEEKS 4 GEEKS - gate cs mock 2018
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix ? 7/4 1/7 7 4/7 Answer given : 7/4 My answer : 7 trace of a matrix is the sum of its diagonal elements.So on transposing the matrix the diagonal elements will ... is also equal to sum of eigen values.So trace of A = 7 So trace of transpose(A) should be 7. Is my reasoning right?
vk_9_1_9
asked
in
Linear Algebra
Jan 3, 2019
by
vk_9_1_9
1.2k
views
matrix
0
votes
0
answers
159
Wiki example - Rouché–Capelli_theorem
What is the rank of the augmented matrix and coefficient matrix here ? x + y + 2z = 3, x + y + z = 1, 2x + 2y + 2z = 2 The example says it’s Augmented Matrix Rank is 3 and Coefficent Matrix Rank is 2, Can someone share the solution using echelon Form? This is a question from wiki page example here
Salazar
asked
in
Set Theory & Algebra
Jan 1, 2019
by
Salazar
216
views
matrix
rank-of-matrix
discrete-mathematics
4
votes
1
answer
160
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 = $ $5I+A$ $5I-A$ $A-5I$ $6I$
Ruturaj Mohanty
asked
in
Linear Algebra
Dec 27, 2018
by
Ruturaj Mohanty
936
views
go-mockgate-1
engineering-mathematics
linear-algebra
matrix
6
votes
5
answers
161
TIFR CSE 2019 | Part A | Question: 15
Consider the matrix $A = \begin{bmatrix} \frac{1}{2} &\frac{1}{2} & 0\\ 0& \frac{3}{4} & \frac{1}{4}\\ 0& \frac{1}{4} & \frac{3}{4} \end{bmatrix}$ What is $\displaystyle \lim_{n→\infty}$A^n$ ? $\begin{bmatrix} \ 0 ... $\text{The limit exists, but it is none of the above}$
Arjun
asked
in
Calculus
Dec 18, 2018
by
Arjun
2.8k
views
tifr2019
engineering-mathematics
calculus
limits
matrix
2
votes
1
answer
162
NIELIT 2018-21
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigen vector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is $15$ $16$ $17$ $18$
Arjun
asked
in
Linear Algebra
Dec 7, 2018
by
Arjun
2.2k
views
nielit-2018
engineering-mathematics
linear-algebra
matrix
eigen-value
3
votes
1
answer
163
NIELIT 2018-30
If $C$ is a non-singular matrix and $B=C \begin{bmatrix} 0 & x & y \\ 0 & 0 & x \\ 0 & 0 & 0 \end{bmatrix} C^{-1}$ then: $B^2=I$ $B^2 = \text{Null Matrix}$ $B^3=I$ $B^3 = \text{Null Matrix}$
Arjun
asked
in
Linear Algebra
Dec 7, 2018
by
Arjun
1.3k
views
nielit-2018
engineering-mathematics
linear-algebra
matrix
3
votes
1
answer
164
Cases when LU decomposition is possible.
I had already visited below link but was unable to grasp it. https://math.stackexchange.com/questions/218770/when-does-a-square-matrix-have-an-lu-decomposition. I made some form of self-analysis, let me know if I am in the correct ... pivot, and if such cannot be fixed without a row shuffle operation, then LU decomposition is not possible. Am I correct?
Ayush Upadhyaya
asked
in
Linear Algebra
Nov 18, 2018
by
Ayush Upadhyaya
3.8k
views
linear-algebra
matrix
2
votes
0
answers
165
Zeal Test Series 2019: Linear Algebra - Matrices
Prince Sindhiya
asked
in
Linear Algebra
Nov 17, 2018
by
Prince Sindhiya
372
views
zeal
linear-algebra
discrete-mathematics
matrix
zeal2019
1
vote
0
answers
166
Linearity of Matrix
$1)$What is linearly independent solution? Why it is depend on rank of matrix? (Linearly independent solution = no of rows of matrix- rank of matrix) $I=N-R$ $2)$ Why for unique solution of a matrix , determinant of matrix need to be nonzero? What should be determinant value for infinite solution?
srestha
asked
in
Linear Algebra
Nov 16, 2018
by
srestha
1.2k
views
matrix
0
votes
0
answers
167
Derive formula of the Matrix
How formula $Ae=e$ is valid? Can someone give an example? Here that formula is used here but I gavenot got clearity how this formula can be correct?
srestha
asked
in
Linear Algebra
Nov 9, 2018
by
srestha
327
views
matrix
1
vote
1
answer
168
Find Inverse
Inverse of this matrix $\begin{bmatrix} 2 &1 &1 \\ 3 &2 &1 \\ 2& 1 &2 \end{bmatrix}$ will be A)$\begin{bmatrix} 3 &-4 &-1 \\ -1 &2 &0 \\ -1 &1 &1 \end{bmatrix}$ B)$\begin{bmatrix} 3 &-1 &-1 \\ -4 &2 &1 \\ -1& 0 &1 \end{bmatrix}$
srestha
asked
in
Linear Algebra
Nov 3, 2018
by
srestha
1.1k
views
engineering-mathematics
matrix
1
vote
0
answers
169
LINEAR ALGEBRA
IF A=$\begin{bmatrix} 2& -0.1\\ 0 & 3 \end{bmatrix}$ AND A-1=$\begin{bmatrix} \frac{1}{2}& a\\ 0 & b \end{bmatrix}$ then a+b ? a)$\frac{7}{20}$ b)$\frac{3}{20}$ c)$\frac{19}{60}$ d)$\frac{11}{20}$
altamash
asked
in
Linear Algebra
Oct 27, 2018
by
altamash
574
views
matrix
2
votes
2
answers
170
Linear algebra
For matrix $p=\begin{bmatrix} 3 &-2 &2 \\ 0 &-2 &1 \\ 0& 0 & 1 \end{bmatrix}$if one of the eigen values is equal to – 2, then which of the following is an eigen vector? (a) [ 3 −2 1 ] (b) [ −3 2 −1 ] (c) [ 1 −2 3 ] (d) [ 5 2 0 ]
sahil_malik
asked
in
Linear Algebra
Oct 21, 2018
by
sahil_malik
2.3k
views
matrix
linear-algebra
1
vote
0
answers
171
Virtual Gate Test Series: Linear Algebra - Eigen Value
Prince Sindhiya
asked
in
Linear Algebra
Oct 16, 2018
by
Prince Sindhiya
536
views
engineering-mathematics
linear-algebra
matrix
eigen-value
virtual-gate-test-series
3
votes
2
answers
172
Virtual Gate Test Series: Linear Algebra - Rank Of The Matrix
Prince Sindhiya
asked
in
Linear Algebra
Oct 15, 2018
by
Prince Sindhiya
1.3k
views
engineering-mathematics
linear-algebra
matrix
rank-of-matrix
virtual-gate-test-series
2
votes
0
answers
173
Virtual Gate Test Series: Linear Algebra - Eigen Values of a Unity Matrix
Prince Sindhiya
asked
in
Linear Algebra
Oct 15, 2018
by
Prince Sindhiya
693
views
engineering-mathematics
linear-algebra
matrix
eigen-value
virtual-gate-test-series
5
votes
5
answers
174
Eigen Value
An orthogonal matrix A has eigen values 1, 2 and 4. What is the trace of the matrix
aditi19
asked
in
Linear Algebra
Sep 20, 2018
by
aditi19
6.9k
views
matrix
eigen-value
0
votes
0
answers
175
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that $trace \: A = det \: A =3$, then what is the trace of $A^{-1}$? $1$ $1/3$ $1/6$ $1/2$
go_editor
asked
in
Linear Algebra
Sep 15, 2018
by
go_editor
604
views
isi2017-mma
engineering-mathematics
linear-algebra
matrix
0
votes
0
answers
176
ISI2017-MMA-15
The diagonal elements of a square matrix $M$ are odd integers while the off-diagonals are even integers. Then $M$ must be singular $M$ must be nonsingular there is not enough information to decide the singularity of $M$ $M$ must have a positive eigenvalue
go_editor
asked
in
Linear Algebra
Sep 15, 2018
by
go_editor
366
views
isi2017-mma
engineering-mathematics
linear-algebra
matrix
0
votes
0
answers
177
ISI2017-MMA-20
The number of ordered pairs $(X, Y)$, where $X$ and $Y$ are $n \times n$ real, matrices such that $XY-YX=I$ is $0$ $1$ $n$ infinite
go_editor
asked
in
Linear Algebra
Sep 15, 2018
by
go_editor
481
views
isi2017-mma
engineering-mathematics
linear-algebra
matrix
0
votes
1
answer
178
ISI2016-MMA-4
The $a, b, c$ and $d$ ... $(a+d)(b+c)$ equals $-4$ $0$ $16$ $-16$
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
418
views
isi2016-mmamma
linear-algebra
matrix
system-of-equations
3
votes
1
answer
179
ISI2016-MMA-18
Let $A=\begin{pmatrix} -1 & 2 \\ 0 & -1 \end{pmatrix}$, and $B=A+A^2+A^3+ \dots +A^{50}$. Then $B^2 =1$ $B^2 =0$ $B^2 =A$ $B^2 =B$
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
288
views
isi2016-mmamma
linear-algebra
matrix
summation
1
vote
2
answers
180
ISI2016-MMA-19
Let $A$ be a real $2 \times 2$ matrix. If $5+3i$ is an eigenvalue of $A$, then $det(A)$ equals 4 equals 8 equals 16 cannot be determined from the given information
go_editor
asked
in
Linear Algebra
Sep 13, 2018
by
go_editor
617
views
isi2016-mmamma
linear-algebra
matrix
eigen-value
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