Consider the matrix 4 -1 1 -2 -3 A = 2 -2 2 2 4047 -1 3 -6 6 -4 -7 7 (a) Find a basis for the null space. (b) Write the solution to Ax = (94-5-6) as a sum of the homogeneous and a particular solution.

Consider the following matrix: 1 -2 3 0 −3 A-3 6 -9 09 -2 5-9 -2 9 Give a basis for each of im(A) and null(A). Number of Vectors: 1 {} Basis for im(A) Number of Vectors: 1 {} Basis for null(A) 0

[-10 -2 -2 -13 -2 -4 -13] P with rational entries and a diagonal matrix D such that D = PT AP. Let A P = 00 00 000 I -2 -4 Find an orthogonal matrix D= 01 00 000 Note: You'll probably need to do a little bit of extra work to ensure that each entry in P is a rational number.

Please solve this question in handwriting. Again please need it in handwriting.

Find the rank and the nullity of the matrix rank (A) = nullity (A) = = rank(A) + nullity (A) = choose > A = -1 -2 -1 -2 -1 3 0 -1 -2 -1 2-5 TT 3 -8

solve all 132