good hand writing plz 11. (8 points) Let T:R + RP be given by the matrix...
Question 5 For each given vector b and matrix A, determine if b e im(A) 1 -2 3 (a) b 0 A 21 3 0 5 15 (b) b A2-24 9 Question 6 Find the rank and nullity of the given linear transformations T and determine which are one-to-one and which are onto. r+ y ri+r2 Question 7 Find nullity(T) if (a) T:R R2, rank(T) 1 (b) T:RR, rank(T) 0 (c) T : Rs ? R2, rank(T)-1 Question 8 Let...
Question 1: Given the following matrix A. 02 A- 1 2 3 2 (a) Find the determinant of A (b) Find eigenvalues and the corresponding eigenspaces of A (c) Determine whether A is diagonalizable. If so, find a matrix P and a diagonal matrix D such that P-1AP=D If not, justify your answer. (d) Find a basis of Im(A) and find the rank of Im(A) (e) Find a basis of Ker(A) and find the rank of Ker(A) Question 1: Given...
please solve both as other did wrong plz 8. [0/5 Points] DETAILS PREVIOUS ANSWERS LARLINALG8 7.1.021. Find the characteristic equation and the eigenvalues (and corresponding eigenvectors) of the matrix. 2 -2 0 3 -2 0 - 1 2 (a) the characteristic equation (2 – 2)(a – 4)(a − 1) X (b) the eigenvalues (Enter your answers from smallest to largest.) (11,12,13) = ( (1,2,4) the corresponding eigenvectors x1 = (1, - 2,9) X2 = (0,2, - 2) x X3 =...
three small problem!!!!! Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
Let T:R? → Rº be the linear transformation that first rotates points clockwise through 30° (7/6 radians) and then reflects points through the line y = 2. Find the standard matrix A for T. A=
Please explain in clear hand writing 6.1. Find the echelon form of the given matrix A, and find its null space N(A) ii. A= /2 4 0 2 3 0 3 3 1 5 2 7 9 7 2 10 0 6 5 3
Q1: If (u,v) = (((,,a,,a,), (1;,6,63)) = a,b – a,b, + a,b; show that (u, v) is inner product or not. Q2: Find a basis and dimension for the Kernel and Image of linear transformation T:R — > R3 given by the formula T(x,y,z) = (x + y, x – y + x,y + 22), and show that dim(ker T) + dim(Im T) = n Q3: Find the matrix P that diagonalize A and then compute P-AP and A20. 1...
for (a) plz thank u!!? 14. For it is given that 1-2 is an invertible matrix such that 1 0 01 AQ A-2 0 0 0 1 0] Let A ((1. 2,0), (0,0, D), (0,0, 0)). Find a basis B of R3 such that the m transition from B to A is matrix of 10 01 D2-0 1 0 and an invertible P such that PAQ D2. (Hint: See the proof of Theorem 3.46.) 15. For each matrix A below,...
linear algebra Find the coordinate matrix of x in RP relative to the basis B'. B' = {(1, -1, 2, 1), (1, 1, -4,3), (1, 2, 0,3), (1, 2, -2, 0)}, x = (16, 10,-8, 7) [x]B 11