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Construct a_{2 2} matrix, where a_v={(i-2j)^2}{2}

Question

Construct $a_{2 \times 2}$ matrix, where $a_{v} = \frac{( i - 2 j ) ^{2}}{2}$

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Construct

a_{2 \times 2}

matrix, where

a_{v} = \frac{( i - 2 j ) ^{2}}{2}

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

We know that, the notation, namely

A [a_{v}]_{m \times n}

indicates that

A

is a matrix order

m \times n

, also

1 \leq i \leq m, 1 \leq j \leq n; i, j \in N

.
Here,

A = [a_{v}]_{m \times n}

\Rightarrow A = \frac{( i - 2 j ) ^{2}}{2}, 1 \leq i \leq 2, 1 \leq j \leq 2.... (i)

∴ a_{11} = \frac{( 1 - 2 ) ^{2}}{2} = \frac{1}{2}

∴ a_{12} = \frac{( 1 - 2 \times 2 ) ^{2}}{2} = \frac{9}{2}

∴ a_{21} = \frac{( 2 - 2 \times 1 ) ^{2}}{2} = 0

∴ a_{22} = \frac{( 2 - 2 \times 2 ^{2} ) ^{2}}{2} = 2

Thus,

A = [\frac{1}{2} 0 \frac{9}{2} 0]_{2 \times 2}

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Question Text	Construct $a_{2 \times 2}$ matrix, where $a_{v} = \frac{( i - 2 j ) ^{2}}{2}$
Answer Type	Text solution:1
Upvotes	150