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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
Find inverse for given matrix A-1="\\begin{bmatrix}\n 5& 4\\\\\n 9& 7\n\\end{bmatrix}"
Solve the following system of linear equations for ๐ฅ, ๐ฆ, ๐ง, ๐ก: โ๐ฆ+3๐ง+2๐ฅ+4๐ก = 9
๐ฅโ2๐ง+7๐ก =11 ๐งโ3๐ฆ+3๐ฅ+5๐ก = 8 ๐ฆ + 2๐ฅ + 4๐ง + 4๐ก = 10
Let W={(x,y,z)|x+y+z=0}
a, give a basis for W
b, what is the dimension of W
Show that the set of vectors {(1,1,5),(1,1,3),(1,1,3)} is linear independent or not
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, ๐ด๐ฅ=๐๐ฅ, 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 ๐^((0))=5 and ๐^((1))=4 Solve for the eigenvalues by the QR method
Let W be the set of vector space in R3 of the form (a,b, ยฝa-2b) show that W is the sub space of R3
