Register

CMI-2021-DataScience-B: 10

• retagged by
227 views
0 votes
0 votes
Let $A$ be the $3 \times 3$ real matrix $\left(\begin{array}{lll} a & b & c \\ d & e & f \\ g & h & I \end{array}\right)$. Suppose $x^{T} Ax \geq 0$ for every $x \in \mathbb{R}^{3}$. Then show that all of $a, e$ and $i$ are non-negative.
• retagged by
User Avatar

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 votes
0 votes
0 answers
1
admin asked Jul 23, 2022
212 views
CMI-2021-DataScience-B: 5
Show that every selection of $503$ numbers from $\{1,2,3, \dots,987\}$ has two numbers with g.c.d. $1$. Recall that the g.c.d. of two positive integers $x, y$ is the largest positive integer smaller than $x, y$ which divides both $x$ and $y$.
Show that every selection of $503$ numbers from $\{1,2,3, \dots,987\}$ has two numbers with g.c.d. $1$. Recall that the g.c.d. of two positive integers $x, y$ is the larg...
User Avatar
0 votes
0 votes
0 answers
2
admin asked Jul 23, 2022
193 views
CMI-2021-DataScience-A: 10
Let $A, B$ be $n \times n$ matrices. Which of the following properties of $A$ and $B$ is/are preserved under matrix multiplication? Being upper triangular. All diagonal elements being zero. Being diagonal. Being symmetric.
Let $A, B$ be $n \times n$ matrices. Which of the following properties of $A$ and $B$ is/are preserved under matrix multiplication?Being upper triangular.All diagonal ele...
User Avatar
Link Copied!