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and Consider the matrices [1 2 3 4] 1 1 1 1 A= lo -1 0 1 14 34 31 17 7777 1 2 3 4 . Which of the B= lo -1 0 1 La 34 35 following is true? det B = - det A det B = det A det B = -7 det A det B = 7 det A
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear operators LB, Lo. b) Using part a), find a basis for R3 that diagonalizes the linear operators c) Write B- EDE- with D a diagonal matrix. d) Find the eigenvalues, eigenspaces, and generalized eigenspaces of LA
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear...
1 -1 Let A= -1 -2 1 1 singular value decomposition A = U£VT (a) Find a (b) Determine the pseudoinverse matrix At, expressing At single matrix. as a (c) Consider the equation ) Ax 1 = and find the least squares approximation x' with minimum norm
1 -1 Let A= -1 -2 1 1 singular value decomposition A = U£VT (a) Find a (b) Determine the pseudoinverse matrix At, expressing At single matrix. as a (c) Consider the equation...
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts) (b) (+37). ū (4 pts) (c) The vector of magnitude 5 that points in the same direction as (4 pts). (d) The angle between 7 and ū (4 pts). (e) Find Projz() (4 pts).
(7.2:al) Let 10 -9 10 10 Find Condı(A) 10-10 11 10)-find the bound . If A is changed to A' on the relative change of z in 1-norm » Find the actual relative change of r in 1-norm · If b is changed to b, 0 , find the bound on the relative change of r in 1-norm Find the actual relative change of r in 1-norm. (7.2:a2)Let 10-9 10 10 . Find Condo(A) . If A is changed to...
Fourth Homework (1) Let P-(**.0) and Q ( . (a) Find the pole of the line PQ (b) Find the parametrization of the line PQ (c) Does (ch,顽週lie on the line PQ? 克,2 7, ) lie on the line PQ? (2) Find the distance between the lines (1,0,-1) + t(2,3,0) and m (2,-1,3) +s(0, 1,2). (3) Let A and B be two distinct points of S2. Show that X e I d(X, A) = d(X, b)) is a line and...
(1) Let 7 =< 2,1,-2 > and 7 =< 1,2,3 >. Find two vectors and such that ✓ = 7+7, where is parallel to 7 and is orthogonal to 7.
These are linear algebra problems.
1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
Linear Algebra
2) General Inner Products, Length, Distance and Angle a) Determine if (u,v)-3uiv,-u,v, is a dot product b) Show that (u.v)-a+a,h,'2 is a product if a, 20 e)Let A-(41 ..)and B-G ) Use inner product on 4 -2 M (A, B aitai +apb +2a to find the length of A, B, namely ll-41 and 1 d) Find the angle between the two matrices above e) Find the distance between the two above matrices 0) For the functions (x)-1 and...
5. Find the vector 5 that is parallel to vector a = 27 -7 and has the length of 5. 6. Find the distance between two points (-1,-3,6) and (0,3,0). 7. Find the distance from the point (-5,3,-2) to a. the origin b. the x-axis c. the xz-plane 8. Let P; be the midpoint of the line segment between P.(-3,4,1) and P2(-5,8,3). Find the coordinate of the midpoint between P, and P3. 9. Knowing = (2,-3,1), 7 = (-2,0,5), and...