Explain the question in steps Linear Algebra #2. Solve, x_(1)+x_(3)-x_(4)=1, 2x_(1)+x_(3)+x_(4)=0, 3x_(1)+2x_(3)=1.
(A) [[1+2t],[2s],[3+t],[1-t]]
(B) [[-1+2t],[1+2s],[3+t],[t]]
(C) [[-1-2t],[s],[3+t],[t]]
(D) [[-1-2t],[s],[2+3t],[t]]
(E) None of the above
#3. Find all values of constant k such that T is invertible with A=[[3,k],[2,-4]].
(A) k<0
(B) k!=7.5
(C) k!=-6
(D) k>0
(E) None of the above
#4. Let L be the line containing the vector [[4],[-3]]. Find the orthogonal projection of the vector x=[[1],[-1]] onto L. (use the formula: projL(x)=(x*u)u, where u is contained in L,||u||=1)
#5. Find the reflection of [[1],[0],[1]] about the line L in the direction of the vector [[-3],[0],[4]]. (Use the formula ref Lx=2(x*u)u-x, where u is contained in L,||u||=1)
(A) [[(31)/(25)],[(13)/(25)],[(17)/(25)]]
(B) [[(31)/(25)],[0],[-(17)/(25)]]
(C) [[-(31)/(25)],[0],[-(17)/(25)]]
(D) None of the above
#6. Let M=[[1,2,0]][[2],[0],[1]],N=[[2],[0],[1]][[1,2,0]]. Find M and N.
#7. Matrix A=[[0.8,-0.6],[0.6,0.8]] represents a rotation through an angle θ in the counterclockwise direction. Find the angle θ. (Use the formula [[cosθ,-sinθ],[sinθ,cosθ]])
