Explanation Given: The provided expression is [ − 1 0 1 0 − 1 0 0 1 1 ] [ x y z ] = [ − 4 2 4 ] Formula used: If linear system of equation is given as [ a 1 a 2 a 3 b 1 b 2 b 3 c 3 c 2 c 3 ] [ x y z ] = [ d 1 d 2 d 3 ] Then above system of equation can be represented as a 1 x + b 1 y + c 1 z = d 1 , a 2 x + b 2 y + c 2 z = d 2 , a 3 x + b 3 y + c 3 z = d 3 Calculation: Consider the system equations: [ − 1 0 1 0 − 1 0 0 1 1 ] [ x y z ] = [ − 4 2 4 ] The linear system can be written as: A X = B [ − 1 0 1 0 − 1 0 0 1 1 ] [ x y z ] = [ − 4 2 4 ] Where, A = [ − 1 0 1 0 − 1 0 0 1 1 ] X = [ x y z ] B =

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Author: ROBERT BLITZER

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Chapter 9.4, Problem 36E

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To calculate: The matrix [−1010−10011][xyz]=[−424] in the linear system equation.

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Chapter 9.4, Problem 35E

Chapter 9.4, Problem 37E

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

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]

part b please

Chapter 9 Solutions

MyLab Math with Pearson eText -- Combo Access Card (18-wk) for Algebra & Trigonometry

Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Prob. 3CVC Ch. 9.1 - Prob. 4CVC Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - Fill in each blank so that the resulting statement...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...Ch. 9.1 - In Exercises 18, write the augmented matrix for...Ch. 9.1 - In Exercises 1-8, write the augmented matrix for...

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The matrix [ − 1 0 1 0 − 1 0 0 1 1 ] [ x y z ] = [ − 4 2 4 ] in the linear system equation.

Solution Summary: The author explains how the linear system of equation can be written as: underset_c-x+z=-4 -y=2

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To calculate: The matrix [−1010−10011][xyz]=[−424] in the linear system equation.

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Chapter 9 Solutions