Calculus: Single And Multivariable
7th Edition
ISBN: 9781119444190
Author: Hughes-Hallett, Deborah; Mccallum, William G.; Gleason, Andrew M.; Connally, Eric; Kalaycioglu, Selin; Flath, Daniel E.; Lahme, Brigitte; Lomen, David O.; Lock, Patti Frazer; Lovelock, David; Morris, Jerry; Lozano, Guadalupe I.; Mumford, David; Quinney, D
Publisher: WILEY
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Textbook Question
Chapter 14.1, Problem 22E
Approximate fx (3, 5) using the contour diagram of f(x, y) in Figure 14.9.
Figure 14.9
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4. Suppose that A is made up of 5 column vectors in R³, and suppose that the
rank(A)=3.
a. How many solutions are there to Ax=0? Justify.
b. What is a geometric description for the nullspace(A)? Justify.
c. Do the column vectors of A span R³? Justify.
d. Is A invertible? Justify.
3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following.
a. Give a geometric description of nullspace(A). Justify.
b. Is A invertible? Justify.
c. Give a geometric description of the span of the column vectors of A. What
space are the column vectors of A in? Justify.
d. What is determinant of A? Justify.
2. Consider the matrix:
A
||
1
1
-3
14
2 1 01
4 1
2
2
-26
1 -3
1 5]
a) What is rank(A)?
b) Is A invertible? Justify.
c) Find the nullspace(A). Justify.
d) Is the trivial solution the only solution to Ax=0? Justify.
e) What is the span of the column vectors of A? Justify.
Chapter 14 Solutions
Calculus: Single And Multivariable
Ch. 14.1 - Using dierence quotients, estimate fx(3, 2) fy(3,...Ch. 14.1 - Prob. 3ECh. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - In Exercises 1015, a point A is shown on a contour...Ch. 14.1 - Approximate fx (3, 5) using the contour diagram of...Ch. 14.1 - Figure 14.11 shows the contour diagram of g(x, y)...Ch. 14.1 - Figure 14.13 shows the saddle-shaped surface z =...Ch. 14.2 - Prob. 2ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 8E
Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 27ECh. 14.2 - Prob. 39ECh. 14.2 - Prob. 65ECh. 14.2 - Which of the following functions satisfy the...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 18, nd the equation of the tangent...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 912, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1316, nd the dierential of the...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - In Exercises 1720, assume points P and Q are...Ch. 14.3 - Prob. 23ECh. 14.3 - In Exercises 2124, assume points P and Q are...Ch. 14.3 - The tangent plane to z = f(x, y) at the point (1,...Ch. 14.3 - Find an equation for the tangent plane to z = f(x,...Ch. 14.3 - (a). Find the equation of the plane tangent to the...Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 114, nd the gradient of the function....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 1522, nd the gradient at the point....Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - In Exercises 2328, which of the following vectors...Ch. 14.4 - Prob. 45ECh. 14.4 - Prob. 48ECh. 14.4 - In Exercises 5051, nd the dierential df from the...Ch. 14.4 - In Exercises 5253, nd grad f from the dierential....Ch. 14.4 - In Problems 5864, nd the quantity. Assume that g...Ch. 14.4 - For f(x,y)=(x+y)/(1+x2) nd the directional...Ch. 14.4 - Let f(x, y) = x2y3. At the point (1, 2), nd a...
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