Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Chapter 11.7, Problem 25PS
To determine
The absolute extrema of
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6. The domain of y = v1-x2 is
8. Decide which of the following sets are linearly independent in R". Justify your
answer in each case.
(a) X₁ = {(1,0), (0, 1)} ℃ R²
(b) X₂ = {(1,0), (2,0)} ℃ R²
(c) X3 = {(-1,0), (0, 0)} CR²
2
(d) X₁ = {(1,0), (0, 1), (1, 1)} ℃ R²
C
(e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} ℃ R³
(f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³
(g) X7 = {(0, 0, 0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³
(h) Xs = {(0, 1, 0), (1, 1, 1)} ℃ R³
8
(i) X9 = {(4,3,0,0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4
(j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rª
8. Decide which of the following sets are linearly independent in R". Justify your
answer in each case.
(a) X₁ = = {(1,0), (0, 1)} ℃R²
(b) X₂ = {(1,0), (2,0)} CR²
(c) X3 =
{(-1,0), (0,0)} ℃ R²
(d) X4 =
{(1,0), (0, 1), (1, 1)} C R²
(e) X5 = {(1,0,0), (0, 1, 0), (1, 1, 1)} CR³
(f) X6 = {(1,0,0), (0, 1, 0), (1, 1, 1), (−1, 0, 1)} ℃ R³
(g) X7 = {(0,0,0), (0, 1, 0), (1, 1, 1), (–1, 0, 1)} ℃ R³
(h) X8 = {(0, 1,0), (1, 1, 1)} C R³
(i) X9 = {(4, 3, 0, 0), (0, 0, 1, 1), (0, 0, 0, 1), (1, 0, 0, 1), (0, 1, 0, 1)} ℃ R4
(j) X10 = {(1, 2, 0, 0), (0, 2, 3, 0), (0, 0, −1, 1)} ℃ Rª
9. Decide, for the sets X; above, for which i, j = {1, 2, ..., 10}, span(X₂) = span(X;).
Chapter 11 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 11.1 - Prob. 1PSCh. 11.1 - Prob. 2PSCh. 11.1 - Prob. 3PSCh. 11.1 - Prob. 4PSCh. 11.1 - Prob. 5PSCh. 11.1 - Prob. 6PSCh. 11.1 - Prob. 7PSCh. 11.1 - Prob. 8PSCh. 11.1 - Prob. 9PSCh. 11.1 - Prob. 10PS
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Prob. 51PSCh. 11.6 - Prob. 52PSCh. 11.6 - Prob. 53PSCh. 11.6 - Prob. 54PSCh. 11.6 - Prob. 55PSCh. 11.6 - Prob. 56PSCh. 11.6 - Prob. 57PSCh. 11.6 - Prob. 58PSCh. 11.6 - Prob. 59PSCh. 11.6 - Prob. 60PSCh. 11.7 - Prob. 1PSCh. 11.7 - Prob. 2PSCh. 11.7 - Prob. 3PSCh. 11.7 - Prob. 4PSCh. 11.7 - Prob. 5PSCh. 11.7 - Prob. 6PSCh. 11.7 - Prob. 7PSCh. 11.7 - Prob. 8PSCh. 11.7 - Prob. 9PSCh. 11.7 - Prob. 10PSCh. 11.7 - Prob. 11PSCh. 11.7 - Prob. 12PSCh. 11.7 - Prob. 13PSCh. 11.7 - Prob. 14PSCh. 11.7 - Prob. 15PSCh. 11.7 - Prob. 16PSCh. 11.7 - Prob. 17PSCh. 11.7 - Prob. 18PSCh. 11.7 - Prob. 19PSCh. 11.7 - Prob. 20PSCh. 11.7 - Prob. 21PSCh. 11.7 - Prob. 22PSCh. 11.7 - Prob. 23PSCh. 11.7 - Prob. 24PSCh. 11.7 - Prob. 25PSCh. 11.7 - Prob. 26PSCh. 11.7 - Prob. 27PSCh. 11.7 - Prob. 28PSCh. 11.7 - Prob. 29PSCh. 11.7 - Prob. 30PSCh. 11.7 - Prob. 31PSCh. 11.7 - Prob. 32PSCh. 11.7 - Prob. 33PSCh. 11.7 - Prob. 34PSCh. 11.7 - Prob. 35PSCh. 11.7 - Prob. 36PSCh. 11.7 - Prob. 37PSCh. 11.7 - Prob. 38PSCh. 11.7 - Prob. 39PSCh. 11.7 - Prob. 40PSCh. 11.7 - Prob. 41PSCh. 11.7 - Prob. 42PSCh. 11.7 - Prob. 43PSCh. 11.7 - Prob. 44PSCh. 11.7 - Prob. 45PSCh. 11.7 - Prob. 46PSCh. 11.7 - Prob. 47PSCh. 11.7 - Prob. 48PSCh. 11.7 - Prob. 49PSCh. 11.7 - Prob. 50PSCh. 11.7 - Prob. 51PSCh. 11.7 - Prob. 52PSCh. 11.7 - Prob. 53PSCh. 11.7 - Prob. 54PSCh. 11.7 - Prob. 55PSCh. 11.7 - Prob. 56PSCh. 11.7 - Prob. 57PSCh. 11.7 - Prob. 58PSCh. 11.7 - Prob. 59PSCh. 11.7 - Prob. 60PSCh. 11.8 - Prob. 1PSCh. 11.8 - Prob. 2PSCh. 11.8 - Prob. 3PSCh. 11.8 - Prob. 4PSCh. 11.8 - Prob. 5PSCh. 11.8 - Prob. 6PSCh. 11.8 - Prob. 7PSCh. 11.8 - Prob. 8PSCh. 11.8 - Prob. 9PSCh. 11.8 - Prob. 10PSCh. 11.8 - Prob. 11PSCh. 11.8 - Prob. 12PSCh. 11.8 - Prob. 13PSCh. 11.8 - Prob. 14PSCh. 11.8 - Prob. 15PSCh. 11.8 - Prob. 16PSCh. 11.8 - Prob. 17PSCh. 11.8 - Prob. 18PSCh. 11.8 - Prob. 19PSCh. 11.8 - Prob. 20PSCh. 11.8 - Prob. 21PSCh. 11.8 - Prob. 22PSCh. 11.8 - Prob. 23PSCh. 11.8 - Prob. 24PSCh. 11.8 - Prob. 25PSCh. 11.8 - Prob. 26PSCh. 11.8 - Prob. 27PSCh. 11.8 - Prob. 28PSCh. 11.8 - 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