TS EAMCET 2020 (Online) 10th September Evening Shift | Matrices and Determinants Question 111 | Mathematics

A is a $m \times n$ matrix of rank 4 . If A contains an $m$ th order non singular sub matrix and $A^T A$ is a $7 \times 7$ matrix, then the number of rows of $A$ is

TS EAMCET 2020 (Online) 10th September Evening Shift

MCQ (Single Correct Answer)

-0

If $C$ and $D$ are two $n \times n$ non-singular matrices over the set of real number $\mathbf{R}$ such that $C D=-D C$, then $n$ is

a natural number of the form $3 k+5, k \in \mathbf{N}$

an odd integer

$n$ even integer

equal to one

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

If $A, B$ are two non singular matrices of order $3,|B|=k$, a positive integer, then match the items of list-I with the items of list-II.

$$ \text { List-I } $$		$$ \text { List-II } $$
A.	$\quad\left\|k^{-1} A^{-1}\right\|$	I.	$$ B A^k+A^k B $$
B.	$\left\|\operatorname{Adj}\left(A^{-1}\right)\right\|$	II.	$$ \frac{B \operatorname{Adj}(B)}{\|B\|} $$
C.	$B A B^{-1}=I, \Rightarrow B A^k B^{-1}=$	III.	$$ \frac{1}{\|B\|^3\|A\|} $$
D.	$\quad \operatorname{Adj}\left(\operatorname{Adj}\left(A^{-1}\right)\right)=$	IV.	$$ \frac{1}{\|A\|}\left(A^{-1}\right) $$
		V.	$$ \frac{1}{\|A\|^2} $$

$$ \text { The correct match is } $$

A	B	C	D
III	V	II	IV

A	B	C	D
III	IV	I	II

A	B	C	D
I	V	II	IV

A	B	C	D
III	IV	II	I

TS EAMCET 2020 (Online) 10th September Morning Shift

MCQ (Single Correct Answer)

-0

All the real values of $p, q$ so that the system of equations

$$ 2 x+p y+6 z=8, x+2 y+q z=5 $$

and $\quad x+y+3 z=4$

may have no solution are

$p=2, q \neq 3$

$p=2, q=\frac{15}{2}$

$p \neq 2, q=3$

$p=3, q=\frac{15}{4}$

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