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Recent questions tagged rank-of-matrix
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GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 22
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following is/are always true? The rank of $A$ is 12. The ranks of $A$ and $B$ are ... . If $v$ is a vector such that $A v=0$ then $B v$ is also 0. The rank of $B$ is at most 11.
Let $A$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $A$, we get a matrix $B$ which has 12 nonzero rows. Which of the following i...
GO Classes
326
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GO Classes
asked
Feb 5
Linear Algebra
goclasses2024-mockgate-14
linear-algebra
rank-of-matrix
multiple-selects
1-mark
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7
votes
2
answers
2
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 7
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. Which of the following is/are always true? The rank of $\text{A}$ ... that $\text{A} v=0$ then $\text{B} v$ is also $0.$ The rank of $\text{B}$ is at most $11.$
Let $\text{A}$ be a $20 \times 11$ matrix with real entries. After performing some row operations on $\text{A}$, we get a matrix $\text{B}$ which has $12$ nonzero rows. W...
GO Classes
571
views
GO Classes
asked
Jan 21
Linear Algebra
goclasses2024-mockgate-12
goclasses
linear-algebra
rank-of-matrix
multiple-selects
1-mark
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9
votes
2
answers
3
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 5
Suppose that the characteristic polynomial of $\text{A}$ is $ p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2. $ Which of the following can you determine from this information? The rank of $\text{A}$. Whether $\text{A}$ is symmetric. Whether $\text{A}$ is diagonalizable. The eigenvalues of $\text{A}$.
Suppose that the characteristic polynomial of $\text{A}$ is$$p(\lambda)=\lambda(\lambda-2)(\lambda-3)^2.$$Which of the following can you determine from this information?T...
GO Classes
767
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
goclasses
linear-algebra
eigen-value
rank-of-matrix
multiple-selects
1-mark
+
–
8
votes
2
answers
4
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 10
Let $A=\begin{pmatrix}1 & 2 & 1 & 0 & 0 \\ 1 & 2 & 2 & 2 & 3 \\ -1 & -2 & 0 & 2 & 3\end{pmatrix}$ What will be the $\text{rank(A)}?$ $1$ $2$ $3$ $5$
Let $A=\begin{pmatrix}1 & 2 & 1 & 0 & 0 \\ 1 & 2 & 2 & 2 & 3 \\ -1 & -2 & 0 & 2 & 3\end{pmatrix}$What will be the $\text{rank(A)}?$$1$$2$$3$$5$
GO Classes
618
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GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
goclasses
linear-algebra
rank-of-matrix
1-mark
+
–
17
votes
2
answers
5
GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 20
Consider Three matrices $A, B$ and $C$ ... $\alpha_1$, then: The Entries which are not shown in matrices are zeros. What is the rank of $B ?$
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{...
GO Classes
995
views
GO Classes
asked
Apr 5, 2023
Linear Algebra
goclasses2024_wq7
numerical-answers
goclasses
linear-algebra
rank-of-matrix
2-marks
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3
votes
3
answers
6
Made Easy: Linear Algebra (MSQ)
Let $A$ be a $3$ x $3$ matrix with rank $2$. Then, $AX=0$ has The trivial solution $X=0$. One independent solution. Two independent solution. Three independent solution.
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.
DebRC
1.0k
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DebRC
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Sep 19, 2022
Linear Algebra
linear-algebra
engineering-mathematics
rank-of-matrix
matrix
system-of-equations
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–
1
votes
1
answer
7
TIFR CSE 2022 | Part B | Question: 14
Let $G$ be a directed graph (with no self-loops or parallel edges) with $n \geq 2$ vertices and $m$ edges. Consider the $n \times m$ incidence matrix $M$ of $G$, whose rows are indexed by the vertices of $G$ and the columns by the edges of $G$ ... . Then, what is the rank of $M?$ $m-1$ $m-n+1$ $\lceil m / 2\rceil$ $n-1$ $\lceil n / 2\rceil$
Let $G$ be a directed graph (with no self-loops or parallel edges) with $n \geq 2$ vertices and $m$ edges. Consider the $n \times m$ incidence matrix $M$ of $G$, whose ro...
admin
433
views
admin
asked
Sep 1, 2022
Graph Theory
tifr2022
graph-theory
graph-connectivity
rank-of-matrix
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13
votes
1
answer
8
TIFR CSE 2022 | Part A | Question: 8
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the $(n+1)$-th row of $A$ has every entry equal to $-n^2$ ... $A$ has rank $n$ $A^2$ has rank $1$ All the eigenvalues of $A$ are distinct All the eigenvalues of $A$ are $0$ None of the above
Let $A$ be the $(n+1) \times(n+1)$ matrix given below, where $n \geq 1$. For $i \leq n$, the $i$-th row of $A$ has every entry equal to $2i-1$ and the last row, i.e., the...
admin
652
views
admin
asked
Sep 1, 2022
Linear Algebra
tifr2022
linear-algebra
rank-of-matrix
eigen-value
+
–
3
votes
2
answers
9
GO Classes Test Series 2023 | Linear Algebra | Test | Question: 10
What could be the possible values of $\operatorname{rank}(\mathrm{A})$ as "$a$" varies: $ A=\left[\begin{array}{ccc} 1 & 2 & a\\ -2 & 4 a & 2\\ a & -2 & 1 \end{array}\right] $ For some value ... $a$, rank could be $1$ For some value of $a$, rank could be $2$ For some value of $a$, rank could be $3$
What could be the possible values of $\operatorname{rank}(\mathrm{A})$ as "$a$" varies:$$A=\left[\begin{array}{ccc}1 & 2 & a\\-2 & 4 a & 2\\a & -2 & 1\end{array}\right]$$...
GO Classes
373
views
GO Classes
asked
Aug 14, 2022
Linear Algebra
goclasses2024-la-weekly_quiz
goclasses
linear-algebra
rank-of-matrix
multiple-selects
2-marks
+
–
2
votes
1
answer
10
TIFR CSE 2021 | Part A | Question: 3
Let $M$ be an $n \times m$ real matrix. Consider the following: Let $k_{1}$ be the smallest number such that $M$ can be factorized as $A \cdot B$, where $A$ is an $n \times k_{1}$ and $B$ is a $k_{1} \times m$ matrix. Let $k_{2}$ be the smallest number ... $k_{1}= k_{2}= k_{3}$ No general relationship exists among $k_{1}, k_{2}$ and $k_{3}$
Let $M$ be an $n \times m$ real matrix. Consider the following:Let $k_{1}$ be the smallest number such that $M$ can be factorized as $A \cdot B$, where $A$ is an $n \time...
soujanyareddy13
625
views
soujanyareddy13
asked
Mar 25, 2021
Linear Algebra
tifr2021
linear-algebra
matrix
rank-of-matrix
+
–
43
votes
14
answers
11
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T...
Arjun
18.0k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
+
–
2
votes
1
answer
12
TIFR CSE 2020 | Part A | Question: 2
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x> 0.$ Then Such an $M$ cannot exist Such $Ms$ exist and their rank is always $n$ Such $Ms$ exist, but their eigenvalues are always real No eigenvalue of any such $M$ can be real None of the above
Let $M$ be a real $n\times n$ matrix such that for$ every$ non-zero vector $x\in \mathbb{R}^{n},$ we have $x^{T}M x 0.$ ThenSuch an $M$ cannot existSuch $Ms$ exist and th...
admin
1.4k
views
admin
asked
Feb 10, 2020
Linear Algebra
tifr2020
engineering-mathematics
linear-algebra
rank-of-matrix
eigen-value
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