Prealgebra (hardcover) (8th Edition)
Prealgebra (hardcover) (8th Edition)
8th Edition
ISBN: 9780134708799
Author: Martin-Gay, Elayn
Publisher: PEARSON
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Chapter C, Problem 24E

Objectives A B Mixed Practice See Examples 1 and 2. The bar graph below shows estimates of the top six external debts of countries of March 2016. If a number is written in standard form, write it in scientific notation. If a number is written in scientific notation, write it in standard form.

Chapter C, Problem 24E, Objectives A B Mixed Practice See Examples 1 and 2. The bar graph below shows estimates of the top

Use the bar graph to estimate the external debt of the United States and then express it in both standard and scientific notation.

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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}

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Prealgebra (hardcover) (8th Edition)

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