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Recent questions tagged rank-of-matrix

47 votes
14 answers
31
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...
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0 votes
0 answers
33
ISI2015-MMA-40
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ ... $(\textbf{A})$ equals $1$ or $2$ $0$ $4$ $2$ or $3$
Let $x_1, x_2, x_3, x_4, y_1, y_2, y_3$ and $y_4$ be fixed real numbers, not all of them equal to zero. Define a $4 \times 4$ matrix $\textbf{A}$ by$$\textbf{A} = \begin{...
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3 votes
4 answers
34
ISI2018-MMA-12
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
The rank of the matrix$\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$$1$$2$$3$$4$
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4 votes
2 answers
35
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)
Nullity of a matrix = Total number columns – Rank of that matrixBut how to calculate value of x when nullity is already given(1 in this case)
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0 votes
1 answer
37
Rank of the matrix
Given that a matrix $[A]_{4\times4},$any one row/column is dependent on the others, and given matrix are singular matrix$(|A|=0)$. And another matrix $B=adj(A),$then find them, $1)$Rank of the matrix $B$ $2)$Rank of the marix $adj(B)$
Given that a matrix $[A]_{4\times4},$any one row/column is dependent on the others, and given matrix are singular matrix$(|A|=0)$.And another matrix $B=adj(A),$then find ...
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0 votes
0 answers
39
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{pmatrix}$ is 2 for some real numbers $a$ and $b$. Then the $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix $\begin{pmatrix} 1 & 1 & 2 & 2 \\ 1 & 1 & 1 & 3 \\ a & b & b & 1 \end{pmatrix}$ is 2 for some real numbers $a$ and $b$. Then the $b$ equals...
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2 votes
1 answer
40
ISI2016-MMA-28
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true? $A \neq A^2$ Eigenvalues of $A^2$ are all zero rank($A$) > rank($A^2$) rank($A$) > trace($A$)
Let $A$ be a square matrix such that $A^3 =0$, but $A^2 \neq 0$. Then which of the following statements is not necessarily true?$A \neq A^2$Eigenvalues of $A^2$ are all z...
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0 votes
1 answer
41
Rank of a matrix
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE? (a) Rank of BA is less than 2. (b) Rank of BA is equal to 2. (c) Rank of BA is greater than 2. (d) Rank of BA can be any number between 1 and 3.
Let A be a 4×3 real matrix with rank 2. Let B be transpose matrix of A. Which one of the following statement is TRUE?(a) Rank of BA is less than 2.(b) Rank of BA is equa...
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10 votes
8 answers
42
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$
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8 votes
3 answers
43
ISI2017-MMA-5
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$?$1$$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{6}\right)$$\left(\dfr...
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0 votes
1 answer
44
IE Gate 2007
Let $A$ = $[a_{ij}]$, $1{\leq}i$, $j{\leq}n$, with $n{\geq}3$ and $a_{ij}$ = $i.j$. Then the rank of $A$ is A. $0$ B. $1$ C. $n-1$ D. $n$
Let $A$ = $[a_{ij}]$, $1{\leq}i$, $j{\leq}n$, with $n{\geq}3$ and $a_{ij}$ = $i.j$. Then the rank of $A$ isA. $0$B. $1$C. $n-1$D. $n$
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6 votes
1 answer
45
Made easy books GATE - 2015( IN ) 1 mark
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is $A)$ $r$ $B)$ $n$ $C)$ $n - r $ $D)$ $n + r$
Let $A$ be a $n\times n$ matrix with rank $ r ( 0 < r < n ) .$Then $AX = 0$ has $p$ independent solutions,where $p$ is$A)$ $r$ $B)$ $n$ $C)$ $n - r...
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3 votes
0 answers
47
rank of matrix
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix. (A) Always true (B) Sometimes true (C) False (D) None of the above
The rank of the matrix of coefficients of a homogeneous system of m linear equations in n unknowns is never less than the rank of the augmented matrix.(A) Always true(B) ...
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2 votes
1 answer
48
Rank of matrix
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.
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1 votes
1 answer
49
GF MT 4
Is the answer and explaination given correct ?
Is the answer and explaination given correct ?
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0 votes
2 answers
50
ACE-MockTest:Matrix algebra-Rank
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6 votes
2 answers
51
ISRO2014-72
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ . $0$ $1$ $2$ $3$
The rank of the matrix $A=\begin{pmatrix} 1 & 2 & 1 & -1\\ 9& 5& 2& 2\\ 7& 1& 0 & 4 \end{pmatrix}$ is ______ .$0$$1$$2$$3$
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0 votes
2 answers
52
Gate 2008 Ee
Answer given as option a ) My knowledge . Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zero linearly independent solution = n-r n--> no of unknowns r---> rank therefore linerly independent solution = 5-4 = 1 What is linerly independent Rows ... ? linerly independent vectors ?
Answer given as option a )My knowledge .Rank of a matrix Q is 4 implies 1 out of 5 rows of Q is zerolinearly independent solution = n-rn no of unknownsr - ranktherefore ...
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24 votes
7 answers
53
GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is $$ \begin{bmatrix} 1 & a & a^2 & \dots & a^n \\ 1 & a & a^2 & \dots & a^n \\ \vdots ...
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18 votes
4 answers
54
GATE CSE 1994 | Question: 1.9
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is: $0$ $1$ $2$ $3$
The rank of matrix $\begin{bmatrix} 0 & 0 & -3 \\ 9 & 3 & 5 \\ 3 & 1 & 1 \end{bmatrix}$ is:$0$$1$$2$$3$
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20 votes
4 answers
55
GATE CSE 1998 | Question: 2.1
The rank of the matrix given below is: $\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$ $3$ $1$ $2$ $4$
The rank of the matrix given below is:$$\begin{bmatrix} 1 &4 &8 &7\\ 0 &0& 3 &0\\ 4 &2& 3 &1\\ 3 &12 &24 &21 \end{bmatrix}$$$3$$1$$2$$4$
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