The positive value of the determinant of the matrix A, whose A d … - Vidyadip

MCQ

The positive value of the determinant of the matrix $A$, whose $A d j(A d j(A))=\left(\begin{array}{ccc}14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right)$, is

A
$13$
✓
$14$
C
$15$
D
$16$

✓

Answer

Correct option: B.

$14$

b
$\operatorname{Adj}(\operatorname{Adj} A)=\left[\begin{array}{ccc}14 & 18 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right]$

$|\operatorname{Adj}(\operatorname{Adj} A)|=\left[\begin{array}{ccc}14 & 28 & -14 \\ -14 & 14 & 28 \\ 28 & -14 & 14\end{array}\right]=14 \times 14 \times 14\left|\begin{array}{ccc}1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1\end{array}\right|$

$=(14)^{3}[3-2(-5)-1(-1)]=(14)^{3}[14]=(14)^{4}$

$|A|^{4}=(14)^{4} \Rightarrow|A|=14$

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

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If the integral $\int {\frac{{\cos \,8x + 1}}{{\cot \,2x - \tan \,2x}}} dx = A\,\cos \,8x + k,$ where $k$ is an arbitrary constant, then $A$ is equal to

$\int_{}^{} {{e^x}\frac{{({x^2} + 1)}}{{{{(x + 1)}^2}}}dx = } $

Find $\lambda$ and $\mu$ if $(2 \hat{i}+6 \hat{j}+27 \hat{k}) \times(\hat{i}+\lambda \hat{j}+\mu \hat{k})=\overrightarrow{0}$

Let a curve $y=f(x)$ pass through the point $\left(2,\left(\log _{e} 2\right)^{2}\right)$ and have slope $\frac{2 y}{x \log _{e} x}$ for all positive real value of $x$. Then the value of $f(e)$ is equal to $.....$

What is the magnitude of vector -3i + 5j:

If the events $A$ and $B$ are mutually exclusive, then $P\left( {\frac{A}{B}} \right) = $

$f(x) = {x^2} - 3x$, then the points at which $f(x) = f'(x)$ are

If $A = \left| {\,\begin{array}{*{20}{c}}{ - 1}&2&4\\3&1&0\\{ - 2}&4&2\end{array}\,} \right|$and $B = \left| {\,\begin{array}{*{20}{c}}{ - 2}&4&2\\6&2&0\\{ - 2}&4&8\end{array}\,} \right|$, then $B$ is given by

Derivative of ${x^6} + {6^x}$ with respect to $x $ is

The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is: