Linear Algebra with Applications 8th Edition solutions

Linear Algebra with Applications 8
Determine whether the first vector is a linear combination of the other vectors. (a) (-3, 3, 7); (1, -1, 2), (2, 1, 0), (-1, 2, 1) (b) (-2, 11, 7); (1, -1, 0), (2, 1 '4), (-2, 4, 1) (c) (2, 7, 13); (1, 2, 3), (-1, 2, 4), (1, 6, 10)

Linear Algebra with Applications 8
Find all the values of x that make the following determinant zero. x 2x -x 0 x - 1 x - 1 2 4 x + 1

Linear Algebra with Applications 8
Let Ube the set of all vectors in R3 that are perpendicular to a vector u. Prove that U is a vector space.

Linear Algebra with Applications 8
Solve the following equation for x . I x x I --6 2 x - 3

Linear Algebra with Applications 8
A company is buying lockers. It has narrowed the choice down to two kinds, X and Y. X has a volume of 36 cubic feet, while Y has a volume of 44 cubic feet. X occupies an area of 6 square feet and costs $54, while Y occupies 8 square feet and costs $60. A total of 256 square feet of floor space is ava

Linear Algebra with Applications 8
Consider the following input-output matrix that defines the interdependency of five industries. 1 2 3 4 5 1. Auto 0.15 0.10 0.05 0.05 0.10 2. Steel 0.40 0.20 0.10 0.10 0.10 3. Electricity 0.10 0.25 0.20 0.10 0.20 4. Coal 0.10 0.20 0.30 0.15 0.10 5. Chemical 0.05 0.10 0.05 0.02 0.05 Determine (a) the

Linear Algebra with Applications 8
Simplify the determinants of the following matrices by creating zeros in a single row or column, then evaluate the determinant by expanding in terms of that row or column. (a) [ : -:J ) [ j ] (c) [ : - -1 5 6 i

Linear Algebra with Applications 8
Evaluate the determinants of the following matrices (i) using the first row (ii) using the "diagonals" method. (b) [- - ;] 9 1 -1

Linear Algebra with Applications 8
Evaluate the determinants of each of the following matrices in two ways, using the indicated rows and columns. Observe that you get the same answers both ways. (a) [ - ] ) [ - !] lstrow and lstcolumn 3rd row and 2nd column

Linear Algebra with Applications 8
In Exercises 2-6 consider the economies consisting of either two or three industries. Determine the output levels required of each industry in each situation to meet the demands of the other industries and of the open sector. A = [0.30 0.60] ' 0.35 0.10 D = [:!]. [ 1 ]. [ 1 ]. and [ :J in turn

Linear Algebra with Applications 8
Find the fourth-order Fourier approximation to J(x) = 2x - l over[0,2?T].

Linear Algebra with Applications 8
Find values of t for which the following sets are linearly dependent. (a) {(-1, 2), (t, -4)} (b) {{3, t), (6, t - 1)} (c) {{2, -t ), (2t + 6, 4t)}

Linear Algebra with Applications 8
Evaluate the determinants of the following 2 X 2 matrices. (a) [ 2 3 (c) [ _ ] ] (b) [ -] (d) [ _ =!J

Linear Algebra with Applications 8
Graph theory is being used in mathematical models to better understand the delicate balance of nature. Figure 2.29 gives the digraph that describes the food web of an ecological community in the Ocala National Forest, in central Florida. Determine the adjacency matrix. Raccoon Bird Insect Grass Deer

Linear Algebra with Applications 8
Let 2 -3 0 6 1 -4 Find the following minors and cofactors of A. (a) M11 and C11 (b) M21 and C21 (c) Mz3 and C23 (d) M33 and C33

Linear Algebra with Applications 8
Determine the adjacency matrix and the distance matrix of each of the digraphs in Figure 2.27. (b) p1 ------- (c) (d) Figure 2.27

Linear Algebra with Applications 8
Let A = [ -0 -6 1 Find the following minors and cofactors of A. (a) M13 and C13 (b) M22 and C22 (c) M31 and C31 (d) M33 and C33

Linear Algebra with Applications 8
The following tables represent information obtained from questionnaires given to groups of people. In each case construct the digraph that describes the leadership structure within the group. Rank the members according to their influence on the group. (a) Group member Mi M2 M3 M4 (b) Group member Mi

Linear Algebra with Applications 8
Let A be the adjacency matrix of a digraph. What do you know about the digraph in each of the following cases? (a) The third row of A is all zeros. (b) The fourth column of A is all zeros. ( c) The sum of the elements in the fifth row of A is 3. ( d) The sum of the elements in the second column of A

Linear Algebra with Applications 8
In a graph with n vertices what is the greatest possible distance between two vertices.