MCQs of Matrices (Mathematics - I - 3110014)

Mathematics - I (3110014) MCQs

MCQs of Matrices

Showing 1 to 10 out of 44 Questions

Which of the following matrix is in Row Echelon Form?

(a)	$[\begin{matrix} 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 2 & - 4 \end{matrix}]$
(b)	$[\begin{matrix} 0 & 1 & - 4 & 5 \\ 1 & 2 & 3 & 4 \\ 0 & 0 & 0 & 0 \end{matrix}]$
(c)	$[\begin{matrix} 0 & - 2 & 0 & 4 \\ 0 & 0 & 0 & 5 \\ 0 & 0 & 0 & 0 \end{matrix}]$
(d)	$[\begin{matrix} 1 & 2 & 3 & 4 \\ 0 & 0 & - 5 & 7 \\ 2 & 3 & 9 & 0 \end{matrix}]$

Which of the following matrix is in Reduced Row Echelon Form?

(a)	$[\begin{matrix} 1 & 0 & 4 & 6 \\ 0 & 1 & 5 & 7 \\ 0 & 0 & 0 & 1 \end{matrix}]$
(b)	$[\begin{matrix} 1 & 4 & - 3 & 7 \\ 0 & 1 & 6 & 2 \\ 0 & 0 & 1 & 5 \end{matrix}]$
(c)	$[\begin{matrix} 0 & 1 & 0 & 6 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{matrix}]$
(d)	$[\begin{matrix} 1 & 0 & 0 & 4 \\ 0 & 1 & 0 & 7 \\ 0 & 0 & 1 & - 1 \end{matrix}]$

The minimum and maximum eigen values of the matrix $[\begin{matrix} 3 & - 1 & 0 \\ - 1 & 2 & - 1 \\ 0 & - 1 & 3 \end{matrix}]$ are 1 and 4 respectively. What is the other eigen value?

(a)	3
(b)	4
(c)	0
(d)	-2

The rank of the matrix $(\begin{matrix} 1 & 1 & 1 \\ 1 & - 1 & 0 \\ 1 & 1 & 1 \end{matrix})$ is _____.

(a)	0
(b)	1
(c)	2
(d)	3

If A $= [\begin{matrix} - 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 \\ 5 & 7 & 2 & 0 \\ 9 & 1 & 0 & 2 \end{matrix}]$ , then A.M. of 2 is _____.

(a)	1
(b)	2
(c)	3
(d)	5

Which of the following is always true for any square matrix?

(a)	A.M. $\geq$ G.M.
(b)	A.M. $\leq$ G.M.
(c)	A.M. > G.M
(d)	A.M. = G.M.

The system of linear equations $x + 2 y + z = 6, 2 x + y + 2 z = 6 & x + y + z = 5$ has _____.

(a)	no solution
(b)	infinitely many solutions
(c)	unique solution
(d)	finite solution

The eigen values of the matrix $[\begin{matrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{matrix}]$ are given by solving the cubic equation _____.

(a)	$λ^{3} + 7 λ^{2} + 11 λ + 5 = 0$
(b)	$λ^{3} + 7 λ^{2} + 11 λ - 5 = 0$
(c)	$λ^{3} - 7 λ^{2} + 11 λ + 5 = 0$
(d)	$λ^{3} - 7 λ^{2} + 11 λ - 5 = 0$

For what values of $α$ and $β$ the following linear system have an infinite number of solution?

$x + y + z = 5, x + 3 y + 3 z = 9, x + 2 y + α z = β$

(a)	7, 2
(b)	3, 8
(c)	8, 3
(d)	2, 7

10.

Let $ρ (A - 3 I) = 1$ , where $A$ is a square matrix of order 3 . Then G.M. of the eigen value 3 is _____.

(a)	1
(b)	2
(c)	3
(d)	4

Showing 1 to 10 out of 44 Questions