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What is x if matrix determinant d=4? matrix = (2  3)              (4  x)

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realfluf | Student, Undergraduate | (Level 1) eNoter

Posted September 25, 2013 at 4:26 PM via web

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What is x if matrix determinant d=4?

matrix = (2  3)

             (4  x)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 25, 2013 at 4:38 PM (Answer #1)

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You need to evaluate the determinant `|A|` of the given square matrix A, using the following formula, such that:

`A = ((a,b),(c,d))`

`|A| = ad - bc`

Reasoning by analogy, yields:

`A = ((2,3),(4,x))`

`d = |A| = 2x - 4*3 => d = |A| = 2x - 12`

The problem provides the information that the determinant of square matrix is `4` , hence, you need to replace `4` for `|A|` in equation above, such that:

`2x - 12 = 4 => 2x = 12 + 4 => 2x = 16 => x = 8`

Hence, evaluating x, under the given conditions, yields `x = 8.`

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