Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 9.2, Problem 46PS
To determine
To Calculate:
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Please solve
2.
a. In each part express the vector as a linear combination of
2+x+4x², p₂ = 1 − x + 3x², and p3 = 3 + 2x + 5x².
pi
i. -9-7x - 15x²
ii. 6+11x + 6x²
=
iii. O
iv. 7 + 8x + 9x²
b. Suppose that vi
=
= (2, 1, 0, 3), v₂ = (3, −1, 5, 2), and №3 = (–1, 0, 2, 1).
Which of the following vectors are in span {1, 2, 3}?
i.
(2, 3, -7,3)
ii.
(0,0,0,0)
iii. (1,1,1,1)
iv. (-4, 6, -13, 4)
Solve the following exercises, you will need to show all your work to receive full credit. Consider the
matrix,
2 1 -2
2 3 -4
1
1
1
-
Knowing that f(t) = (t – 1)²(t - 2) is the characteristic polynomial, do the following:
1. find a basis of eigenvectors;
2. Find P such that P- AP is a diagonal matrix D. Give D
Chapter 9 Solutions
Calculus
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