-4 | 4 | -4 | 3 | -2 |
4 | -3 | -2 | 2 | 2 |
4 | -2 | 5 | 3 | -5 |
.
convert into Reduced Row Eschelon Form...
Divide row1 by -4
1 | -1 | 1 | -3/4 | 1/2 |
4 | -3 | -2 | 2 | 2 |
4 | -2 | 5 | 3 | -5 |
Add (-4 * row1) to row2
1 | -1 | 1 | -3/4 | 1/2 |
0 | 1 | -6 | 5 | 0 |
4 | -2 | 5 | 3 | -5 |
Add (-4 * row1) to row3
1 | -1 | 1 | -3/4 | 1/2 |
0 | 1 | -6 | 5 | 0 |
0 | 2 | 1 | 6 | -7 |
Add (-2 * row2) to row3
1 | -1 | 1 | -3/4 | 1/2 |
0 | 1 | -6 | 5 | 0 |
0 | 0 | 13 | -4 | -7 |
Divide row3 by 13
1 | -1 | 1 | -3/4 | 1/2 |
0 | 1 | -6 | 5 | 0 |
0 | 0 | 1 | -4/13 | -7/13 |
Add (6 * row3) to row2
1 | -1 | 1 | -3/4 | 1/2 |
0 | 1 | 0 | 41/13 | -42/13 |
0 | 0 | 1 | -4/13 | -7/13 |
Add (-1 * row3) to row1
1 | -1 | 0 | -23/52 | 27/26 |
0 | 1 | 0 | 41/13 | -42/13 |
0 | 0 | 1 | -4/13 | -7/13 |
Add (1 * row2) to row1
1 | 0 | 0 | 141/52 | -57/26 |
0 | 1 | 0 | 41/13 | -42/13 |
0 | 0 | 1 | -4/13 | -7/13 |
reduced system is
.
general solution is
.
null space are
(1 point) Let -6 -12 9-161 A=14 6-6 Find a non-zero vector in the column space of A.
(1 point) Let -6 -12 9-161 A=14 6-6 Find a non-zero vector in the column space of A.
I need all details. Thx
2. Give an example of a matrix with the indicated properties. If the property cannot be attained, explain why not (a) A is 2 x 4 and has rank 3. (b) A is 3 × 3 and has determinant 1. (c) A is 3 × 6 and has a 3 dimensional row space and a 6 dinensional column space (d) A is 3 × 3 and has a 2 dimensional null space. (e) A is...
|(1 point) Let -2 -4 -4 -4 A = -3 -6 -6 -6 Find a spanning set for the null space of A. 1 N(A) span - 0 0
|(1 point) Let -2 -4 -4 -4 A = -3 -6 -6 -6 Find a spanning set for the null space of A. 1 N(A) span - 0 0
1 point) -3 Let A-3 4 14 and b- 12 -12 1 1 -4 -57 -24 Select Answer1. Determine if b is a linear combination of Ai, A2 and A3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation. (A non-trivial relation is three numbers that are not all three zero.) Otherwise, enter O's for the coefficients Ai+ A2t A, b. 1 point) Determine if the given subset of R3 is a...
(1 point) Let A= [-4 0 18 10 1 -3 1 -6 1 -2 0 -4 1 -1 0 -3 4 1 4 -12 8 A basis for the row space of A is { }. vector
(1 point) Let -3 -6 1 -1 -3 3 1 A = -4-3 9 -2 -8 -1 3 6 Find a spanning set for the null space of A N(A) span
(1 point) Let -3 -6 1 -1 -3 3 1 A = -4-3 9 -2 -8 -1 3 6 Find a spanning set for the null space of A N(A) span
[1 -1 0 0 -2 0] 1 4 -4 0 0 -8 0 (1 point) Let A = 10 0 -1 2 -3 3 . Find a basis for the row space of A, a basis for the column space of A, a basis for the null space 0 0 0 -3 0 -2 Lo 0 1 0 3 3] [1 -1 0 0 -2 01 0 0 1 0 3 0 of A, the rank of A, and the...
PART A
PART B
(1 point) Let A [0 3 -6_0] [0[2 -4_6 [ Find a spanning set for the null space of A. e Es m N(A) = span } s (1 point) Let -1 2 -4 3 A 2 12 -4 -9 2 12 -2 -12 -4 4 1 Find a spanning set for the null space of A. !!! III !! N(A) = span
1
Problem 4. Let V be a vector space and let U and W be two subspaces of V. Let (1) Prove that ifU W andWgU then UUW is not a subspace of V (2) Give an example of V, U and W such that U W andWgU. Explicitly verify the implication of the statement in part1). (3) Proue that UUW is a subspace of V if and only if U-W or W- (4) Give an example that proues the...
(1 point) Let 6 -5 5 16 47 5 4 6 A= and b= 3 3 11 -4 -3 -8 116 40 Define the transformation T:R? R4 by T(2) = Ax. Find a vector x whose image under T is b. = Is the vector x unique? unique