Construct a 3 - 4 matrix whose elements a ij are given by a ij - i -2 j183 - 589114 - 6 - 8 - 10 15 - 7 - 9 - 11 lendbmatrix 3 - 5 - 7 - 9 14 - 6 - 8 - 10 15 - 7 - 9 - 1111 e n d b m a t r i x 3 - 5 - 7 - 9 12 - 1 - 0 - 3 12 - 4 - 6 - 8 1lendbmatrix D- Vbeginbmatrix 3 - 5 - 7 - 9 12 - 1 - 0 - 3 15 - 7 - 9 - 11endbmatrix

The correct option is B [ 3 amp; 5 amp; 7 amp;9; 4 amp; 6 amp; 8 amp; 10; 5 amp; 7 amp; 9 amp; 11; ] The elements of a 3 × 4 ...

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Standard X

Mathematics

Matrix Definition and Representation

Construct a 3...

Question

Construct a $3 \times 4$ matrix whose elements $a_{i j}$ are given by $a_{i j} = i + 2 j$

$⎡ ⎢ ⎣ \begin{matrix} 1 & 3 & 5 & 9 4 & 6 & 8 & 10 5 & 7 & 9 & 11 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 3 & 5 & 7 & 9 2 & 1 & 0 & 3 2 & 4 & 6 & 8 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 3 & 5 & 7 & 9 2 & 1 & 0 & 3 5 & 7 & 9 & 11 \end{matrix} ⎤ ⎥ ⎦$

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$⎡ ⎢ ⎣ \begin{matrix} 3 & 5 & 7 & 9 4 & 6 & 8 & 10 5 & 7 & 9 & 11 \end{matrix} ⎤ ⎥ ⎦$

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Solution

The correct option is D
$⎡ ⎢ ⎣ \begin{matrix} 3 & 5 & 7 & 9 4 & 6 & 8 & 10 5 & 7 & 9 & 11 \end{matrix} ⎤ ⎥ ⎦$

The elements of a $3 \times 4$ matrix are $A = ⎡ ⎢ ⎣ \begin{matrix} a_{11} & a_{12} & a_{13} & a_{14} a_{21} & a_{22} & a_{23} & a_{24} a_{31} & a_{32} & a_{33} & a_{34} \end{matrix} ⎤ ⎥ ⎦$

Applying the given rule: $a_{i j} = i + 2 j a_{11} = 3, a_{12} = 5, a_{13} = 7, a_{14} = 9 a_{21} = 4, a_{22} = 6, a_{23} = 8, a_{24} = 10 a_{31} = 5, a_{32} = 7, a_{33} = 9, a_{34} = 11$

Therefore $A = ⎡ ⎢ ⎣ \begin{matrix} 3 & 5 & 7 & 9 4 & 6 & 8 & 10 5 & 7 & 9 & 11 \end{matrix} ⎤ ⎥ ⎦$ is the required matrix.

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Similar questions

If
A = {1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

C = {6, 7, 8, 9}

D = {7, 8, 9, 10}

$\begin{matrix} C o l u m n A & C o l u m n B 1. A \cup B & a . {3, 4, 6, 7} 2. A \cap B & b . \emptyset 3. (B \cap C) \cup D & c . {3, 4} 4. B \cup C \cup D & d . {3, 4, 5, 6, 7, 8, 9, 10} 5. (A \cap B) \cap (B \cup C) & e . {1, 2, 3, 4, 5, 6, 7} f . {6, 7, 8, 9, 10} g . {7} \end{matrix}$

Q. Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1

How many times is number 9 preceded by 1 and succeeded by 7 which is not followed by 5 ?

\begin{matrix} 7 & 9 & 8 & 6 & 5 & 4 + & 1 & 0 & 3 & 0 & 8 & 7 \end{matrix}

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Q. Study the following number line and answer the questions that follow.
2 5 9 1 7 2 5 1 9 7 3 9 5 2 4 6 8 1 9 7 5 2 7 3 1 9 7 8 5 2 6 5 4 1 9 7 8 2 0 1 0 9 7 8 5 1 9 7 3 5 1 6 9 7 2 1 7 3 7 9 5 1

How many times is number '3' preceded by number '7' and not followed by an even number?

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

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Construct a 3×4 matrix whose elements aij are given by aij=i+2j

Construct a $3 \times 4$ matrix whose elements $a_{i j}$ are given by $a_{i j} = i + 2 j$