Explanation Given Information: The provided matrix is [ 4 1 0 2 ] . Formula used: Determinant of a 2 × 2 matrix [ a b c d ] is a d − b c where a , b , c and d are arbitrary numbers. Inverse of a 2 × 2 matrix A = [ a b c d ] is, A − 1 = 1 a d − b c [ d − b − c a ] Where, a , b , c and d are arbitrary numbers. A matrix with m rows and n columns is of dimension m × n , where m and n are positive integers. Calculation: Consider the matrix [ 4 1 0 2 ] . Since, number of rows in [ 4 1 0 2 ] is 2 and number of columns is 2. Thus, dimension of [ 4 1 0 2 ] is 2 × 2 . Now, compare [ 4 1 0 2 ] and [ a b c d ] . Thus, a = 4 , b = 1 , c = 0 and d = 2 . Substitute 4 for a , 1 for b , 0 for c and 2 for d in a d − b c , a d − b c = ( 4 ) ( 2 ) − ( 1 ) ( 0 ) = 8 − 0 = 8 Thus, determinant of [ 4 1 0 2 ] is 8

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 5.3, Problem 28E

To determine

To calculate: The value of the determinant and if the determinant is non-zero, find the inverse of the matrix [4102].

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Chapter 5.3, Problem 27E

Chapter 5.3, Problem 29E

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Chapter 5 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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Ch. 5.1 - Solve for x,y,z,andw. 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The value of the determinant and if the determinant is non-zero, find the inverse of the matrix [ 4 1 0 2 ] .

Solution Summary: The author calculates the determinant and inverse of the matrix left[cc4& 1 0& 2end

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To calculate: The value of the determinant and if the determinant is non-zero, find the inverse of the matrix [4102].

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Chapter 5 Solutions