Construct a 2 × 2 Matrix Whose Elements Aij Are Given By: `A_(Ij)=[[-3i +J]]/2` - Mathematics

प्रश्न

Construct a 2 × 2 matrix whose elements a_ij are given by:

$a_{i j} = \frac{| - 3 i + j |}{2}$

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उत्तर

$a_{i j} = \frac{| - 3 i + j |}{2}$

Here,

$a_{11} = \frac{| - 3 (1) + 1 |}{2} = \frac{| - 3 + 1 |}{2} = \frac{| - 2 |}{2} = 1, a_{12} = \frac{| - 3 (1) + 2 |}{2} = \frac{| - 3 + 2 |}{2} = \frac{| - 1 |}{2} = \frac{1}{2}$

$a_{21} = \frac{| - 3 (2) + 1 |}{2} = \frac{| - 6 + 1 |}{2} = \frac{| - 5 |}{2} = \frac{5}{2}, a_{22} = \frac{| - 3 (2) + 2 |}{2} = \frac{| - 6 + 2 |}{2} = \frac{| - 1 |}{4} = 2$

So, the required matrix is $[\begin{matrix} 1 \frac{1}{2} \\ \frac{5}{2} 2 \end{matrix}]$

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Introduction of Operations on Matrices

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अध्याय 5: Algebra of Matrices - Exercise 5.1 [पृष्ठ ७]

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Exercise 5.1 | Q 5.6 | पृष्ठ ७

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Introduction of Operations on Matrices

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Construct a 2 × 2 Matrix Whose Elements Aij Are Given By: $A_{I j} = \frac{[- 3 i + J]}{2}$ - Mathematics

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