Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 11.7, Problem 26PS
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
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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- 3. If z = f(x, y) with the relation xy²z³ + x®y²z+1= x + y+ z. Find at (1, 1, 1).arrow_forwardDetermine whether the following sets are linearly dependent or linearlyindependent. (a) {(; )( )} . -9} in Maxa(R) 4 (b) {(- ).(- 9G -)} in M2x2(R) 4 (c) {x 3 + 2x2, -x2 + 3x + 1, x3 – x2 + 2x – 1} in P3(R) (d) {x 3 – x, 2x2 + 4, -2x3 + 3x2 + 2x + 6} in P3(R) (e) {(1, -1, 2), (1, -2, 1), (1, 1, 4)} in R3 (f) {(1, –1, 2), (2, 0, 1), (–1, 2, –1)} in R3 {(÷ ) ( -) (; 0. 2 ).(- )} in Max2(R) (g) (m) {(-; ') (? ). -2)} in M2x2(R) () (x 4 - х3 + 5x2 - 8х + 6, -х4 + х3 - 5х2 + 5х - 3, x 4 + 3x2 – 3x + 5, 2x4 + 3x3 + 4x2 – x + 1, x3 – x + 2} in P4(R) ) (x4 - х3 + 5x2 - 8х + 6, -х4 + x3 - 5x2 + 5х - 3, х4 + 3x2 - 3х + 5, 2х4 + х3 + 4x2 + 8х} in P4(R)arrow_forwardProblem 6. Consider the set X = {(x, y) ER ×R: (y≤ x² and x > 0) or (y ≥ r² and x 0, we define X₁ = {(x, x² — ax), x≤ R}. (a) On the same drawing as above, represent X0, X₁ and X₂. (b) Prove that where we recall that, by definition, X = U Xa [0,+∞0) U X₁ = {(x, y) = R XR : € [0, +∞) s.t. (x,y) € Xa}. [0,+∞0)arrow_forward
- 4. f(r, y) +y+ ry,find fay and fyzarrow_forward4.6. Consider the linear program minimize z = 2x1 - 3x2 subject to 4x1+3x2 < 12 X1 – 2x2 < 2 X1, X2 0. Represent the point x (1, 1)' as a convex combination of extreme points plus, if applicable, a direction of unboundedness. Find three different representations.arrow_forward6. A flying robot is programed to follow the following three-dimensional position function while navigating an open space with no wind. The displacements in x, y, and z are measured in meters and t in seconds. x(t) = 0.0560t* – 1.200t² + 2.300t + 0.3400 y(t) = 0.6700t3 – 1.570t² z(t) = 0.2200t³ (a) At t = 1.44 s, what angle does the robot's velocity vector, v, make with its acceleration vector, å? Osarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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