column row and nullsp x c O webwork syreduwebwork2MAT 331 sp

column, row and null-sp x c O webwork syr.edu/webwork2/MAT 331 spring 2017 McDermott/Hw 2-8/3/ -3 3 -18 -5 10-40 4-9 34 ls v in Nul(A)? Type \"yes\" or \"no\". ls w in Nul(A)? Type \"yes\" or \"no\". ls x in Nul(A)? Type \"yes or \"no\". I Note: You can earn partial credit on this problem. Preview My Answers Submit Answers Your score was recorded. You have attempted this problem 4 times. You received a score of 100% for this attempt. Your overall recorded score is 100%. You have unlimited attempts remaining. Email instructor

Solution

We will reduce A to its RREF as under:

Multiply the 1st row by -1/3

Add 5 times the 1st row to the 2nd row

Add -4 times the 1st row to the 3rd row

Multiply the 2nd row by 1/5

Add 5 times the 2nd row to the 3rd row

Add 1 times the 2nd row to the 1st row

Then the RREF of A is

1

0

4

0

1

-2

0

0

0

Null (A) is the set of solutions to the equation X = 0. If X = (x,y,z)^T , then this equation is equivalent to x +4z= 0 and y -2z = 0. Then X = z( -4, 2,1)^T so that Null(A) = span{( -4, 2,1)^T }.

Apparently w = (-4,2,1)^T is in Null(A) while v = (5,-3,7)^T and x = (-5,3,4)^T are not in Null(A).

1	0	4
0	1	-2
0	0	0