Explanation Given information: The given matrix is [ cos θ − sin θ sin θ cos θ ] [ x 1 x 2 x 3 y 1 y 2 y 3 ⋯ ] . The matrix A is [ cos θ − sin θ sin θ cos θ ] . The matrix B is [ x 1 x 2 x 3 y 1 y 2 y 3 ] . Calculation: Write the matrix A . A = [ cos θ − sin θ sin θ cos θ ] Substitute 45 ° for θ . A = [ cos 45 ° − sin 45 ° sin 45 ° cos 45 ° ] = [ 1 2 − 1 2 1 2 1 2 ] In above A matrix, interchange the elements on the principal diagonal and change the signs of the off–diagonal elements. A changed = [ 1 2 1 2 − 1 2 1 2 ] Determine the determinant value of matrix A . | A | = [ 1 2 − 1 2 1 2 1 2 ] = ( 1 2 ) ( 1 2 ) − ( 1 2 × − 1 2 ) = 1 2 + 1 2 = 1 Determine the inverse value of A matrix. A − 1 = A changed | A | Substitute [ 1 2 1 2 − 1 2 1 2 ] for A changed and 1 for | A | . A − 1 = [ 1 2 1 2 − 1 2 1 2 ] 1 = [ 1 2 1 2 − 1 2 1 2 ] Determine the value of A − 1 B

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Chapter 16.3, Problem 39E

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Find the new coordinates of the vertices, if the triangle is rotated clockwise about the origin by 45°.

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Chapter 16.3, Problem 38E

Chapter 16.3, Problem 40E

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Chapter 16 Solutions

Basic Technical Mathematics

Ch. 16.1 - For matrices A and B, find A + B. Ch. 16.1 - Prob. 2PE Ch. 16.1 - Prob. 3PE Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E

Ch. 16.1 - Prob. 8E Ch. 16.1 - In Exercises 3–10, determine the value of the...Ch. 16.1 - Prob. 10E Ch. 16.1 - Prob. 11E Ch. 16.1 - Prob. 12E Ch. 16.1 - Prob. 13E Ch. 16.1 - Prob. 14E Ch. 16.1 - Prob. 15E Ch. 16.1 - Prob. 16E Ch. 16.1 - Prob. 17E Ch. 16.1 - Prob. 18E Ch. 16.1 - Prob. 19E Ch. 16.1 - Prob. 20E Ch. 16.1 - Prob. 21E Ch. 16.1 - Prob. 22E Ch. 16.1 - Prob. 23E Ch. 16.1 - Prob. 24E Ch. 16.1 - Prob. 25E Ch. 16.1 - Prob. 26E Ch. 16.1 - Prob. 27E Ch. 16.1 - Prob. 28E Ch. 16.1 - Prob. 29E Ch. 16.1 - Prob. 30E Ch. 16.1 - Prob. 31E Ch. 16.1 - Prob. 32E Ch. 16.1 - Prob. 33E Ch. 16.1 - Prob. 34E Ch. 16.1 - Prob. 35E Ch. 16.1 - Prob. 36E Ch. 16.1 - Prob. 37E Ch. 16.1 - Prob. 38E Ch. 16.1 - Prob. 39E Ch. 16.1 - Prob. 40E Ch. 16.1 - Prob. 41E Ch. 16.1 - Prob. 42E Ch. 16.1 - Prob. 43E Ch. 16.1 - Prob. 44E Ch. 16.2 - Prob. 1PE Ch. 16.2 - Prob. 2PE Ch. 16.2 - Prob. 3PE Ch. 16.2 - Prob. 1E Ch. 16.2 - Prob. 2E Ch. 16.2 - Prob. 3E Ch. 16.2 - Prob. 4E Ch. 16.2 - Prob. 5E Ch. 16.2 - Prob. 6E Ch. 16.2 - 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Find the new coordinates of the vertices, if the triangle is rotated clockwise about the origin by 45 ° .

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Find the new coordinates of the vertices, if the triangle is rotated clockwise about the origin by 45°.

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Chapter 16 Solutions