1 2 0 42 3 40 -80 64 48 -288 40 13 26 21-15 94-13) and 5 10 8-6 365 2 4 0 8 -6 -10 0 13 2-1 3·Let A = C 4 8 3 25 -2 9 5 1 42 3-1 9 10 22846-2 18 4 -4 3 21 3 2 334 15 26-2 14 5 48 -2 -10 -2 8 -8 814 16 28-23 148 36-6 56 (a) Find a basis for Nul (A)nNul (C) (b) Find...
[ 2 4 -2 11 4. (20pts) Consider a matrix A = 3 7 -8 6 and corresponding Col A & Nul A. -2 -5 7 3 Col A is a subspace of Rk and Nul A is a subspace of R'. |(1) Find k and one nonzero-vector in Col A. | (2) Find 1 and one nonzero-vector in Nul A.
5 1 0 Problem 4: LetA = 0 41 . Consider the linear operator LA : R3 → R3 a) Find the characteristic polynomial for LA b) Let V-Null(A 51). V is an invariant subspace for LA. Pick a basis B for V and c) Let W-Null(A 51)2). W is an invariant subspace for LA Pick a basis a for W 0 3 2 use it to find LAlvls and the characteristic polynomial of LAl and use it to find...
Question 3. (20 pts) Let A= -3 9-27 2 -6 4 8 3 -9 -2 2 Find a basis for Col(A) and a basis for Nul(A). Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(A). (3). How do the dimensions of Nul(A) and Col(A) relate to the number of columns of A?
1) Find the rank of A
2) Find the dimensions of Nul(A) and Col(A)
3) How do the dimensions of Nul(A) and Col(A) relate to the
number of columns of A ?
9 3 2 27 18 A 6 9 2 2 Question 4. (15 pts) Let the matrix A be the same as in Question 3. (1). Find the rank of A. (2). Find the dimensions of Nul(A) and Col(.A). (3). How do the dimensions of Nul(A) and Col(A)...
if whoever answers this could be detailed with explanations
please!
1 -3 -2 -5 -14 -6-3-8 -21 2 8.(15 pts. total) M= is row equivalent to -2 6 1 4 5 -9 -2-7 -14 + (1-3 0-1 0 0 0 2 7 2 Pivels L 0 0 0 0 0 0 0 0 0 0 (a) Find k and/ so that Nul Mc R and Col Mc R (b) Without calculations, list rank M and dim Nul M. (c) Find...
+ Question Details 2 1 , and A = | V1 V2 V3 | . Is p in Nul A? Let v,-| 0 2 Yes, p is in Nul A No, p is not in Nul A 5.+ Question Details 2 2 10 2 1 0 30 0 2 41 4 2 16 3 Let A so that an echelon form of A is given by . Find a basis for Col A 1 0 3 1 0 0 0...
For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. 2 3 8-11 A=1-6-6-12 18 4 -3 -20 23 A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A 1 2 02 A=177-21 351~1013-3 3 4 -6 12 3 3 -9 15
0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue
0 4 -1 1 5. Given, A--2 6 -11 L-2 8-3 1 has the characteristic polynomial p(λ)-(x + 2) (z-2)2(z-1) Find the corresponding eigenvector for each eigenvalue
4 ? 31 NW Let A= 3 7 -8 6 a) Find a spanning set of Nul A. How about Col A? b) is ū in Nul A? Is u in Col A? c) is ù in Nul A? Is ū in Col A? d) Is Col A =İR ?