Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)
13th Edition
ISBN: 9780134679884
Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson
Publisher: PEARSON
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Chapter D, Problem 3ES
a Let
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Într-un bloc sunt apartamente cu 2 camere și apartamente cu 3 camere , în total 20 de apartamente și 45 de camere.Calculați câte apartamente sunt cu 2 camere și câte apartamente sunt cu 3 camere.
1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
Vo... V„−1 such that v; ↔ v; if and only if |ji| Є (r,s). Prove that S has exactly k
components, where k is the greatest common divisor of {n, r,s}.
Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
Chapter D Solutions
Intermediate Algebra, Books a la Carte Edition, Plus MyLab Math -- Access Card Package (13th Edition)
Ch. D - 1. Given and find each of the following.
a.
b....Ch. D - Given f(x)=x2+3 and g(x)=x23 find each of the...Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let and Find each of the following.
3.
Ch. D - a Let and Find each of the following.
4.
Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let and Find each of the following.
6.
Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let and Find each of the following.
8.
Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let f(x)=3x+1 and g(x)=x2+2 Find each of the...Ch. D - a Let and Find each of the following.
12.
Ch. D - Let and Find each of the following.
13.
Ch. D - Let f(x)=x23 and g(x)=4x Find each of the...Ch. D - Let f(x)=x23 and g(x)=4x Find each of the...Ch. D - Let f(x)=x23 and g(x)=4x Find each of the...Ch. D - Let f(x)=x23 and g(x)=4x Find each of the...Ch. D - Let f(x)=x23 and g(x)=4x Find each of the...Ch. D - Prob. 19ESCh. D - Prob. 20ESCh. D - Prob. 21ESCh. D - Prob. 22ESCh. D - Prob. 23ESCh. D - Prob. 24ESCh. D - Prob. 25ESCh. D - Prob. 26ESCh. D - For each pair of functions f and g, find (f+g)(x),...Ch. D - Prob. 28ESCh. D - Prob. 29ESCh. D - Prob. 30ESCh. D - Prob. 31ESCh. D - Prob. 32ES
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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]arrow_forwardQuestion 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]arrow_forwardpart b pleasearrow_forward
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