If [ * 20 c 1& , ,1 & , ,1 1& - 2 & - 2 1& , ,3 & , ,1 ] , [ l x … - Vidyadip

MCQ

If $\left[ {\begin{array}{*{20}{c}}1&{\,\,1}&{\,\,1}\\1&{ - 2}&{ - 2}\\1&{\,\,3}&{\,\,1}\end{array}} \right]\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}0\\3\\4\end{array} \right]$, then $\left[ \begin{array}{l}x\\y\\z\end{array} \right]$is equal to

A
$\left[ \begin{array}{l}1\\1\\1\end{array} \right]$
B
$\left[ \begin{array}{l}\,\,\,1\\ - 2\\\,\,\,3\end{array} \right]$
C
$\left[ \begin{array}{l}\,\,\,1\\ - 2\\\,\,\,1\end{array} \right]$
✓
$\left[ \begin{array}{l}\,\,\,\,1\\\,\,\,\,2\\ - 3\end{array} \right]$

✓

Answer

Correct option: D.

$\left[ \begin{array}{l}\,\,\,\,1\\\,\,\,\,2\\ - 3\end{array} \right]$

d
(d) We have, $\left[ {\begin{array}{*{20}{c}}1&1&1\\1&{ - 2}&{ - 2}\\1&3&1\end{array}} \right]\,\,\left[ \begin{array}{l}x\\y\\z\end{array} \right] = \left[ \begin{array}{l}0\\3\\4\end{array} \right]$

$x + y + z = 0$ ......$(i)$

$x - 2y - 2z = 3$ ......$(ii)$

$x + 3y + z = 4$.....$(iii)$

On solving $x = 1,\,y = 2,\,z = - 3$

i.e., $\left[ \begin{array}{l}{\rm{ }}1\\{\rm{ }}2\\ - 3\end{array} \right]$.

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

The probablity of selecting a male or a female is same. If the probability that in an office of n persons (n - 1) males being selected is $\frac{3}{2^{10}},$ the value of n is:

$\int_{\,\pi }^{\,10\pi } {\,|\sin x|dx} $ is

Given a curve $y=7 x-x^3$ and $x$ increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when $x=5$ is

If the area above the $x -$ axis, bounded by the curves $y = {2^{kx}}$ and $x = 0$ and $x = 2$ is $\frac{3}{{\ln 2}},$ then the value of $k$ is

If $f: R \rightarrow R$ is given by $f(x)=x^3+3$, then $f^{-1}(x)$ is equal to:

The function $f(x) = \left[ {\begin{array}{*{20}{c}} {\left| {x\, - \,3} \right|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,}&{,\,\,\,\,x\, \geqslant \,1} \\ {\left( {\tfrac{{{x^2}}}{4}} \right)\, - \,\left( {\tfrac{{3\,x}}{2}} \right)\, + \,\left( {\tfrac{{13}}{4}} \right)}&{,\,\,\,\,x\, < \,1} \end{array}} \right.$ is :

Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is 100 and the profit in the manufacture of a unit of product E is100 and the profit in the manufacture of aunit of product E is 87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?

If $\mathrm{y}=\mathrm{y}(\mathrm{x})$ is the solution of the differential equation, $\mathrm{e}^{\mathrm{y}}\left(\frac{\mathrm{dy}}{\mathrm{dx}}-1\right)=\mathrm{e}^{\mathrm{x}}$ such that $\mathrm{y}(0)=0,$ then $\mathrm{y}(1)$ is equal to

Let $a, b, c$ be positive real numbers. The following system of equations in $x, y$ and $z\ \frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}-\frac{\text{z}^2}{\text{c}^2}=1,$ $\frac{\text{x}^2}{\text{a}^2}-\frac{\text{y}^2}{\text{b}^2}+\frac{\text{z}^2}{\text{c}^2}=1,$ $-\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}+\frac{\text{z}^2}{\text{c}^2}=1$ has:

If $f (x) =$ $\frac{{\ell \,n\,\,\left( {{e^{{x^2}}}\,\, + \,\,2\,\sqrt x } \right)}}{{\sqrt x }}$ is continuous at $x = 0$ , then $f (0)$ must be equal to :