Write the Minor and Cofactor of Element of the First Column of the Following Matrix and Hence Evaluate the Determinant: a = [ − 1 4 2 3 ] - Mathematics

प्रश्न

Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

$A = [\begin{matrix} - 1 & 4 \\ 2 & 3 \end{matrix}]$

उत्तर

$M_{11} = 3$
$M_{21} = 4$
$C_{i j} = {(- 1)}^{i + j} M_{i j}$
$C_{11} = {(- 1)}^{1 + 1} M_{11} = 3$
$C_{21} = {(- 1)}^{2 + 1} M_{21} = - (4) = - 4$
$D = (3 \times - 1) - (4 \times 2) = - 3 - 8 = - 11$

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Minors and Co-factors

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पाठ 6: Determinants - Exercise 6.1 [पृष्ठ १०]

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पाठ 6 Determinants
Exercise 6.1 | Q 1.2 | पृष्ठ १०

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Minors and Co-factors

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Write the Minor and Cofactor of Element of the First Column of the Following Matrix and Hence Evaluate the Determinant: a = [ − 1 4 2 3 ] - Mathematics

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Write the Minor and Cofactor of Element of the First Column of the Following Matrix and Hence Evaluate the Determinant: a = [ − 1 4 2 3 ] - Mathematics

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