Linear Algebra Answers

Use simplex method to maximize 𝑓 = 3𝑥 + 5𝑦 + 4𝑧 subject to the conditions 2𝑥 + 3𝑦 ≤ 18 2𝑥 + 5𝑦 ≤ 10 3𝑥 + 2𝑦 + 4𝑧 ≤ 15 and 𝑥, 𝑦, 𝑧 ≥ 0.

Use simplex method to maximize 𝑓 = 4𝑥 + 5𝑦 subject to the conditions 𝑥 + 2𝑦 ≤ 5 𝑥 − 2𝑦 ≤ 2 −𝑥 + 𝑦 ≤ 2 2𝑥 + 𝑦 ≤ 6 and 𝑥, 𝑦 ≥ 0.

Show that the set 𝑆 = {(1, 0, 1)(1,1, 0)(−1, 0, −1)} is linearly dependent in 𝑉3(𝑅)

You are given the following matrix

 "A=\\left(\\begin{array}{cccc}a & b & c\\\\ d & e & f \\\\g & h & i\\end{array} \\right)."

Which of the following is the determinant of A?

1. "aei+bfg\u2212cdh\u2212ceg\u2212afh\u2212bdi"
2. "aei+bfg+cdh\u2212ceg\u2212afh+bdi"
3. "aei\u2212bfg+cdh\u2212ceg+afh\u2212bdi"
4. "aei+bfg+cdh\u2212ceg\u2212afh\u2212bdi"
5. "\u2212aei\u2212bfg\u2212cdh+ceg+afh+bdi"

Find all real values of λ such that 

"\\left| \\begin{array}{cccc}1 & \\lambda & -1\\\\ 1 & -1 & -\\lambda \\\\ \\lambda & -1 & 1\\end{array} \\right |=0."

1. λ=0
2. "\\lambda=\\sqrt{3}"
3. "\\lambda=-\\sqrt{3}"
4. There is no such λ
5. λ=1

Consider the linear transformations :

f:R^2→R^2 g:R^2→R^2

f (x,y)→(2x-y,3x+y) g(x,y)→(4x-2y,2x+y)

a) Determine the matrix of linear transformation f relative to the basis

{e1=(1,2),e2=(-1,1)}

b)dertimine (fog)(xy)

c) find g^-1

Using matrix method, solve the simultaneous equations {x-3y=3

5x-9y=11

Michael is a bicycle commuter. he has observed that the reduces the time for his 9 km commute by 15 min when he increases his average speed by 3 km/h. what is Michael's faster speed?

Employ the Gauss-Seidel method, solve the system. 10𝑥 + 𝑦 + 𝑧 = 12 2𝑥 + 2𝑦 + 10𝑧 = 14 2𝑥 + 10𝑦 + 𝑧 = 13

Determine all eigenvalues and the corresponding eigenspaces for the matrix 𝐴 = [ −9 4 4 −8 3 4 −16 8 7 ]