Linear Algebra Answers

Solve the set of linear equations by Gaussian elimination method: a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find a.

(A) 1
(B) 4
(C) 5
(D) -1

1 Solve the set of linear equations by the matrix method: a+3b+2c=3, 2a-b-3c= -8, 5a+2b+c=9. Solve for a

(A) 2
(B) 4
(C) 7
(D) 3

Geometrically representation of basis of v=(3,4) when v1(1,0) v2(0,1) v=av1+bv2

Find one vector in R^3 that spans the intersection of U and W where U is the xy-plane, U={(a,b,0)}, and W is the space spanned by the vectors (1,1,1) and (1,2,3).

Consider the differential equation y"-y'-6y=0. show that the substitutions y1=y and y2=y' lead the following system:
y1'=y2, y2'=6y1+y2.
Using the method of diagonalization, solve this system and then solve the original differential equation.

find (1,0,0) x (0,0,1)

Give an example of a linear operator on R^4 which has no eigenvectors

does a system of 438 homogeneous equations in 245 variables always has a solution

Given Matrix A= |123|
|023|
|003|

Find the basis of Col A and the dim of Col A

Use the cross product to find the sine of the angle between the vectors u = (2,8,-2) and v = (2,8,2) .