Construct a 3 2 matrix whose elements are given by a_ i j =1 2 |i… - Vidyadip

MCQ

Construct a $3 \times 2$ matrix whose elements are given by $a_{i j}=\frac{1}{2}|i-3 j|$.

A
$A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{3}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{3}{2}}
\end{array}} \right]$
B
$A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{5}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{1}{2}}
\end{array}} \right]$
✓
$A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{5}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{3}{2}}
\end{array}} \right]$
D
$A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{5}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{5}{2}}
\end{array}} \right]$

✓

Answer

Correct option: C.

$A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{5}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{3}{2}}
\end{array}} \right]$

c
In general a $3 \times 2$ matrix is given by $A\, = \,\left[ {\begin{array}{*{20}{c}}
{{a_{11}}}&{{a_{12}}} \\
{{a_{21}}}&{{a_{22}}} \\
{{a_{31}}}&{{a_{32}}}
\end{array}} \right]$

Now ${a_{ij}} = \frac{1}{2}|i - 3j|,$ $i=1,\,2,\,3$ and $j=1,\,2$

therefore ${a_{11}} = \frac{1}{2}|1 - 3 \times 1|\, = \,1$

${a_{12}} = \frac{1}{2}|1 - 3 \times 2|\, = \,\frac{5}{2}$

${a_{21}} = \frac{1}{2}|2 - 3 \times 1|\, =\,\frac{1}{2}$

${a_{22}} = \frac{1}{2}|2 - 3 \times 2|\, = \,2$

${a_{31}} = \frac{1}{2}|3 - 3 \times 1|\, = \,0$

${a_{32}} = \frac{1}{2}|3 - 3 \times 2|\, = \,\frac{3}{2}$

Hence the required matrix is given by $A\, = \,\left[ {\begin{array}{*{20}{c}}
1&{\frac{5}{2}} \\
{\frac{1}{2}}&2 \\
0&{\frac{3}{2}}
\end{array}} \right]$

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 value of $\int {{e^{2x}}(2\sin 3x + 3\cos 3x)\,\,dx} $ is

A boy tosses fair coin 3 times. If he gets $₹ 2 X$ for $X$ heads, then his expected gain (in ₹) equals to

If $y = y ( x )$ is the solution of the differential equation $\left(1+ e ^{2 x }\right) \frac{ dy }{ dx }+2\left(1+ y ^{2}\right) e ^{ x }=0$ and $y (0)=0$, then $6\left( y ^{\prime}(0)+\left( y \left(\log _{ e } \sqrt{3}\right)\right)^{2}\right)$ is equal to

The differential equation of family of ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}}$ = $c$ is $\left( {y' = \frac{{dy}}{{dx}},\,y'' = \frac{{{d^2}y}}{{d{x^2}}}} \right)$

$\int_{\,0}^{\,3} {\,\frac{{3x + 1}}{{{x^2} + 9}}dx = } $

If $\cos^{-1}\frac{\text{x}}{3}+\cos^{-1}\frac{\text{y}}{2}=\frac{\theta}{2},$ then, $4\text{x}^2-12\text{xy}\cos^2\frac{\theta}{2}+9\text{y}^2=$

If $A = \left[ {\begin{array}{*{20}{c}}4&1\\3&2\end{array}} \right]$and $I = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$, ${A^2} - 6A = $

If the binary operation $\odot$ is defined on the set $Q^+$ of all positive rational numbers by $\text{a}\odot\text{b}=\frac{\text{ab}}4$. Then, $3\odot\Big(\frac{1}5\odot\frac{1}2\Big)$ is equal to:

The parabolas ${y^2} = 4x$ and ${x^2} = 4y$ divide the square region bounded by the lines $x = 4$, $y = 4$ and the coordinate axes. If ${S_1},{S_2},{S_3}$ are respectively the areas of these parts numbered from top to bottom, then ${S_1}:{S_2}:{S_3}$ is

Let $\text{f(x)}=\begin{vmatrix}\cos\text{x}&\text{x}&1\\2\sin\text{x}&\text{x}&2\text{x}\\\sin\text{x}&\text{x}&\text{x}\end{vmatrix},$ then $\lim_\limits{\text{x}\rightarrow0}\frac{\text{f(x)}}{\text{x}^2}$ is equal to: