Register

TIFR ECE 2014 | Question: 7

• recategorized by
549 views
1 1 vote

Let $A$ be an $n \times n$ real matrix. It is known that there are two distinct $n$-dimensional real column vectors $v_{1}, v_{2}$ such that $A v_{1}=A v_{2}$. Which of the following can we conclude about $A?$

  1. All eigenvalues of $A$ are non-negative.
  2. $A$ is not full rank.
  3. $A$ is not the zero matrix.
  4. $\operatorname{det}(A) \neq 0$.
  5. None of the above.

Please log in or register to answer this question.

Answer:
← Previous · TIFR ECE 2014 | Ques...Next → · TIFR ECE 2014 | Ques...
← Previous in category · TIFR ECE 2013 | Ques...Next in category → · TIFR ECE 2014 | Ques...
Position:
Show:
Voting & Accepting an answer helps improve the community

Related questions

1 1 vote
0 0 answers
415
415 views
admin asked Dec 14, 2022
415 views
TIFR ECE 2014 | Question: 5
The matrix\[A=\left(\begin{array}{ccc}1 & a_{1} & a_{1}^{2} \\1 & a_{2} & a_{2}^{2} \\1 & a_{3} & a_{3}^{2}\end{array}\right)\]is invertible when$a_{1}>a_{2}>a_{3}$$a_{1}...
1 1 vote
0 0 answers
347
347 views
admin asked Nov 29, 2022
347 views
TIFR ECE 2017 | Question: 7
A circulant matrix is a square matrix whose each row is the preceding row rotated to the right by one element, e.g., the following is a $3 \times 3$ circulant matrix.\[\l...
1 1 vote
0 0 answers
434
434 views
admin asked Dec 15, 2022
434 views
TIFR ECE 2015 | Question: 13
Let\[A=\left(\begin{array}{ccc}1 & 1+\varepsilon & 1 \\1+\varepsilon & 1 & 1+\varepsilon \\1 & 1+\varepsilon & 1\end{array}\right)\]Then for $\varepsilon=10^{-6}, A$ haso...
1 1 vote
0 0 answers
223
223 views
admin asked Dec 12, 2022
223 views
TIFR ECE 2013 | Question: 12
Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ hasthe same eigenvalues as of $A$ b...

Add Synced Question

×