Explanation Given: The given equation is 2 = 5 x + 1 + 3 x − 1 . Calculation: The equation 2 = 5 x + 1 + 3 x − 1 has a fractional term. The LCD of the equation 2 = 5 x + 1 + 3 x − 1 is ( x + 1 ) ( x − 1 ) . Multiply each term by the LCD. 2 ( x + 1 ) ( x − 1 ) = ( x + 1 ) ( x − 1 ) ( 5 x + 1 + 3 x − 1 ) Simplify the above equation. 2 ( x + 1 ) ( x − 1 ) = 5 ( x − 1 ) + 3 ( x + 1 ) Remove parentheses of the above equation. 2 x 2 − 2 x + 2 x − 2 = 5 x − 5 + 3 x + 3 Combine like term of the above equation. 2 x 2 − 2 = 8 x − 2 The equation 2 x 2 − 2 = 8 x − 2 is not in standard form as the right hand side is not zero. Add − ( 8 x − 2 ) to each side of the equation. 2 x 2 − 2 − ( 8 x − 2 ) = 8 x − 2 − ( 8 x − 2 ) Simplify the above equation...

Beginning Algebra: Early Graphing (4th Edition)

4th Edition

ISBN: 9780134178974

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 9.1, Problem 4QQ

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The equation in standard form and the roots of the quadratic equation.

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Chapter 9.1, Problem 3QQ

Chapter 9.2, Problem 1E

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Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]

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Question 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4

Chapter 9 Solutions

Beginning Algebra: Early Graphing (4th Edition)

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

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Prob. 30PFE Ch. 9 - Prob. 31PFE Ch. 9 - Prob. 32PFE Ch. 9 - The area of a triangle is 68 square meters.The...

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Chapter 9 Solutions