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Recent questions tagged rank-of-matrix

2 votes
1 answer
1
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
asked Feb 10 in Linear Algebra Lakshman Patel RJIT 116 views
0 votes
0 answers
2
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 $3$
asked Sep 23, 2019 in Linear Algebra Arjun 167 views
2 votes
3 answers
3
The rank of the matrix $\begin{bmatrix} 1 &2 &3 &4 \\ 5& 6 & 7 & 8 \\ 6 & 8 & 10 & 12 \\ 151 & 262 & 373 & 484 \end{bmatrix}$ $1$ $2$ $3$ $4$
asked May 11, 2019 in Linear Algebra akash.dinkar12 363 views
4 votes
1 answer
4
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)
asked Jan 24, 2019 in Linear Algebra Nandkishor3939 494 views
0 votes
0 answers
5
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
asked Jan 1, 2019 in Set Theory & Algebra Salazar 45 views
0 votes
1 answer
6
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 $adj(B)$
asked Oct 25, 2018 in Linear Algebra Lakshman Patel RJIT 343 views
0 votes
0 answers
8
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 $1$ $3$ $1/2$ $1/3$
asked Sep 15, 2018 in Linear Algebra jothee 169 views
1 vote
0 answers
9
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($A$)
asked Sep 13, 2018 in Linear Algebra jothee 81 views
0 votes
1 answer
10
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.
asked Jun 21, 2018 in Mathematical Logic bts 586 views
7 votes
6 answers
11
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 $1$ $3$ $1/2$ $1/3$
asked Mar 29, 2018 in Linear Algebra jjayantamahata 919 views
7 votes
3 answers
12
If $A$ is a $2 \times 2$ matrix such that trace $A = det \ A = 3,$ then what is the trace of $A^{-1}$? $1$ $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{2}\right)$
asked Mar 27, 2018 in Linear Algebra jjayantamahata 653 views
0 votes
1 answer
13
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. $n$
asked Mar 4, 2018 in Linear Algebra Prince Sindhiya 105 views
5 votes
1 answer
14
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 $ $D)$ $n + r$
asked Jan 22, 2018 in Linear Algebra Lakshman Patel RJIT 478 views
0 votes
1 answer
16
If the rank of a (5 × 6) matrix Q is 4, then which one of the following statements is correct? (A) Q will have four linearly independent rows and four linearly independent columns (B) Q will have four linearly independent rows and five linearly independent columns (C) QQT will be invertible (D) QTQ will be invertible
asked Nov 16, 2017 in Linear Algebra Manoja Rajalakshmi A 136 views
3 votes
0 answers
17
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
asked Nov 11, 2017 in Linear Algebra Parshu gate 215 views
2 votes
1 answer
18
The rank of above matrix is 3 then what is that square sub matrix of order 3 whose determinant is not equal to 0.
asked Jan 9, 2017 in Linear Algebra harshit agarwal 985 views
1 vote
1 answer
19
Is the answer and explaination given correct ?
asked Jan 7, 2017 in Linear Algebra gatesjt 243 views
0 votes
2 answers
20
0 votes
2 answers
21
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 ?
asked May 3, 2016 in Linear Algebra pC 211 views
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