If A = [ * 20 c 1&2&2 2&1& - 2 &2&b ] is a matrix satisfying the … - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}1&2&2\\2&1&{ - 2}\\a&2&b\end{array}} \right]$ is a matrix satisfying the equation $AA^T=9I $ where$ I$ is $3×3$ identity matrix, then the ordered pair $(a, b)$ is equal to:

✓
$(-2,-1)$
B
$(2,-1)$
C
$(-2,1)$
D
$(2,1)$

✓

Answer

Correct option: A.

$(-2,-1)$

a
${{\rm{A}}{{\rm{A}}^ \top } = 9{\rm{I}}}$

$\left[ {\begin{array}{*{20}{c}}
1&2&2\\
2&1&{ - 2}\\
a&2&b
\end{array}} \right]\left[ {\begin{array}{*{20}{r}}
1&2&{\rm{a}}\\
2&1&2\\
2&{ - 2}&b
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
9&0&0\\
0&9&0\\
0&0&9
\end{array}} \right]$

${{\rm{a}} + 4 + 2{\rm{b}} = 0 \Rightarrow {\rm{a}} + 2{\rm{b}} = - 4}$ ......$(i)$

${2{\rm{a}} + 2 - 2{\rm{b}} = 0 \Rightarrow {\rm{a}} + 2{\rm{b}} = - 1}$ .......$(ii)$

${{\rm{ From (i) and (ii) }}}$

${3{\rm{b}} = - 3 \Rightarrow {\rm{b}} = - 1}$

${{\rm{a}} = - 2}$

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

Given the system of equation $a(x + y + z)=x,b(x + y + z) = y, c(x + y + z) = z$ where $a,b,c$ are non-zero real numbers. If the real numbers $x,y,z$ are such that $xyz \neq 0,$ then $(a + b + c)$ is equal to-

If $f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)$ and $g(x)=f(1) x^2+x f^{\prime}(x)+f^{\prime \prime}(x),$ then the value of $f(4)-g(4)$ is equal to $...........$.

What is the order of the differential equation:
$\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\frac{\text{dy}}{\text{dx}}-\sin^2\text{y}=0.$

Let $y=y(x)$ be the solution of the differential equation $\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x} \log _e x, x>0$ and $y\left(e^{-1}\right)=0$. Then, $y(e)$ is equal to

$\left| {\,\begin{array}{*{20}{c}}{a + b}&{b + c}&{c + a}\\{b + c}&{c + a}&{a + b}\\{c + a}&{a + b}&{b + c}\end{array}\,} \right| = K\,\,\left| {\,\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}\,} \right|\,,$ then $K = $

The differential equation of all straight lines passing through the point $(1,\, - 1)$ is

If vector $a = 2i - 3j + 6k$ and vector $b = - 2i + 2j - k,$ then $\frac{{{\rm{Projection\, of\, vector }} a{\rm{ on\, vector }} b}}{{{\rm{Projection \,of\, vector }} b{\rm { on\, vector }} a}} = $

Number of solution of the equation $\frac{d}{{dx}}\,\,\int\limits_{\cos x}^{\sin x} {\,\,\frac{{dt}}{{1 - {t^2}}}} = 2\sqrt 2 $ in $[0, \pi ]$ is

A function f from the set of natural numbers to the set of integers defined by $\text{f(n)}\begin{cases}\frac{\text{n}-1}{2},&\text{when n is odd}\\-\frac{\text{n}}{2},&\text{when n is even}\end{cases}$ is:

If ${x^2} + {y^2} = t - \frac{1}{t},{x^4} + {y^4} = {t^2} + \frac{1}{{{t^2}}}$ then $\frac{{dy}}{{dx}}$ equals