Intermediate Algebra (13th Edition)
13th Edition
ISBN: 9780134707365
Author: Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson
Publisher: PEARSON
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Chapter D, Problem 2ES
a Let
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Determine whether it's true or false and the reasoning is needed
1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A
reasoning is required.)
(1) Let V be the set of all ordered pairs of real numbers. Consider the following
addition and scalar multiplication operations on u =
u= (u1, u2) and v =
(v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space
under the above operations?
U2
(2) The set Mmxn of all m×n matrices with the usual operations of addition
and scalar multiplication is a vector space.
α
(3) The dimension of the vector space of all matrices A = [a b] in R2×2 with
a+d=0 is 4.
(4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S =
{1, 1+x, x + x2} is [4 -2 1].
(5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.
5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+
f(0).
(a) Find the representing matrix A of L with respect to the ordered basis
{x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2.
(b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the
ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect
to the ordered basis {2,1-x}
Chapter D Solutions
Intermediate Algebra (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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