Download App

Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}6 \\ 3 \\ 2\end{array}\right]$, then the value of $(2 x+y-z)$ is
  • A
    1
  • B
    2
  • C
    3
  • D
    5
✓

Answer

$
\begin{array}{l}\text {}\left[\begin{array}{lll}
1 & 1 & 1 \\
0 & 1 & 1 \\
0 & 0 & 1
\end{array}\right]\left[\begin{array}{l}
x \\
y \\
z
\end{array}\right]=\left[\begin{array}{l}
6 \\
3 \\
2
\end{array}\right] \\
\therefore \quad x+y+z=6 .....(i)\\
\quad y+z=3........(ii) \\
\quad z=2.......(iii) \\
\Rightarrow \quad y+2=3
\end{array}
$
[Using (ii) and (iii)]
$
\begin{array}{l}
\Rightarrow \quad y=1 \\
\Rightarrow \quad x+1+2=6 \\
\Rightarrow \quad x=3
\end{array}
$
[Using (i), (iii) and (iv)]
So, $2 x+y-z=(2 \times 3)+1-2=6+1-2=5$

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 Matrices→Matrices — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A root of the equation $\left| {\,\begin{array}{*{20}{c}}{3 - x}&{ - 6}&3\\{ - 6}&{3 - x}&3\\3&3&{ - 6 - x}\end{array}\,} \right| = 0$ is
→
$\int_{}^{} {{{\cos }^3}{\kern 1pt} x\;{e^{\log (\sin x)}}} \;dx$ is equal to
→
Number of solution of the equation $ 3tanx + x^3 = 2 $  in $ \left( {0,\frac{\pi }{4}} \right)$ is
→
If ${\rm{f}}\left( x \right) = \int\limits_{^{{\pi ^2}/16}}^{{x^2}} {\frac{{\sin x\,\cdot\sin \sqrt \theta  }}{{1 + {{\cos }^2}\sqrt \theta  }}} .d\theta $ then the value of $f ‘$$\left( {\frac{\pi }{2}} \right)$ , is
→
Define a function $f(x)=\frac{16 x^2-96 x+153}{x-3}$ for all real $x \neq 3$. The least positive value of $f(x)$ is
→
In each of the following choose the correct answer:

If A and B are events such that $\text{P}(\text{A}|\text{B})=\text{P}(\text{B}|\text{A}),\ \text{then}:$

→
For a non - zero, real $a, b$ and $c$ $\left| {\begin{array}{*{20}{c}}{\frac{{{a^2} + {b^2}}}{c}}&c&c\\a&{\frac{{{b^2} + {c^2}}}{a}}&a\\b&b&{\frac{{{c^2} + {a^2}}}{b}} \end{array}} \right|$ $= \alpha \, abc$, then the values of $\alpha$ is
→
If ${\sec ^{ - 1}}x = {\rm{cose}}{{\rm{c}}^{ - 1}}y,$ then ${\cos ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}\frac{1}{y} = $
→
Choose the correct answer from given four options in each of the Exercise:
If A, B and C are angles of a triangle, then the determinant $ \begin{vmatrix}-1&\cos\text{C}&\cos\text{B}\\\cos\text{C}&-1&\cos\text{A}\\\cos\text{B}&\cos\text{A}&-1\end{vmatrix}$ is equal to:
  1. 0
  2. -1
  3. 1
  4. None of these.
→
The number of binary operation that can be defined on a set of 2 elements is:
  1. 8
  2. 4
  3. 16
  4. 64
→