Linear Algebra Answers

X+Y-Z=4

2X+Z=7

3X-2Y=5

Find the cofactor for given matrix "\\begin{vmatrix}\n 2& 5\\\\\n 7 & -5\n \n\\end{vmatrix}"

Solve the following system of equations using the method of Gaussian Elimination:

2x +8y + 4z=2

2x +5y + z =5

4x+10y-z=1

Solve the following system of linear equations for 𝑥, 𝑦, 𝑧, 𝑡: −𝑦+3𝑧+2𝑥+4𝑡 = 9

𝑥−2𝑧+7𝑡 =11 𝑧−3𝑦+3𝑥+5𝑡 = 8 𝑦 + 2𝑥 + 4𝑧 + 4𝑡 = 10

Let W={(x,y,z)|x+y+z=0}

a, give a basis for W

b, what is the dimension of W

Write (12,22,1) as a linear combination of the vectors (0,2,1),(3,0,1),(5,6,0) if possible

Consider the linear eigenproblem, 𝐴𝑥=𝜆𝑥, for the matrix

D=[1 1 2

2 1 1

1 1 3 ]

Solve for the largest eigenvalue by the direct method using the secant method. Let 𝜆^((0))=5 and 𝜆^((1))=4 Solve for the eigenvalues by the QR method