Characteristic equation of A = | * 20 c 2&3&0 1&2&5 3& - 1 &2 | i… - Vidyadip

MCQ

Characteristic equation of $A = \left| {\begin{array}{*{20}{c}}
2&3&0\\
1&2&5\\
3&{ - 1}&2
\end{array}} \right|$ is

A
$x^3 - 6x^2 + 18x - 57 = 0$
B
$2x^2 - 12x + 114 = 0$
C
$2x^3 - 12x^2 + 7x - 114 = 0$
✓
$x^3 - 6x^2 + 14x - 57 = 0$

✓

Answer

Correct option: D.

$x^3 - 6x^2 + 14x - 57 = 0$

d
$| A - xI | = 0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\alpha>\beta>\gamma>0$, then the expression
$\cot ^{-1}\left\{\beta+\frac{\left(1+\beta^{2}\right)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{\left(1+\gamma^{2}\right)}{(\beta-\gamma)}\right\}$ $+\cot ^{-1}\left\{\alpha+\frac{\left(1+\alpha^{2}\right)}{(\gamma-\alpha)}\right\}$ is equal to:

$\int_{\,0}^{\,\pi } {\sqrt {\frac{{1 + \cos 2x}}{2}} \,dx} $ is equal to

The area enclosed by the curves $y=\log _{ t }\left( x + e ^{2}\right)$, $x=\log _{ e }\left(\frac{2}{ y }\right)$ and $x =\log _{ e } 2$, above the line $y =1$ is.

The equation to the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is

Let $A$ and $B$ be any two $n \times n$ matrices such that the following conditions hold: $A B=B A$ and there exist positive integers $k$ and $l$ such that $A^k=I$ ( the identity matrix) and $B^l=0$ (the zero matrix). Then,

The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$-axis at a distance $\mathrm{R}$ and $\mathrm{S}(\,>\,\mathrm{R})$ respectively from the origin, is:

If $\int_{\log 2}^x {\frac{{du}}{{{{({e^u} - 1)}^{1/2}}}}} = \frac{\pi }{6}$, then ${e^x} = $

The inequalities represented by the coloured region in figure are...

Maximum slope of the curve $y = - {x^3} + 3{x^2} + 9x - 27$ is

Let $a _1, a _2, a _3, \ldots$ be a $G.P.$ of increasing positive numbers. Let the sum of its $6^{\text {th }}$ and $8^{\text {th }}$ terms be $2$ and the product of its $3^{\text {rd }}$ and $5^{\text {th }}$ terms be $\frac{1}{9}$. Then $6\left( a _2+\right.$ $\left.a_4\right)\left(a_4+a_6\right)$ is equal to