- #1

- 1,196

- 0

See Attachment for Question

See Attachment for Answer from back of book

I do not see how part a and part b are asking me two different things.

I interpret the first part of part a

"Is b in {a_1,a_2,a_3}?"

as

Is b a solution of the system represented by matrix A?

[1,0,-4,4

0,3,-2,1

-2,6,3,-4]

I got up to here

[1,0,-4,4

0,1,-2/3,1/3

0,0,1,-2]

and saw that the system was consistent and stopped and put yes for the first part.

for the second part of part a

"How many vectors are in {a_1,a_2,a_3}?"

I said infinitely many because in the first part of part a I could easily get the matrix in reduced echelon form if I continued and so the fourth column of the matrix could be anything.

For part b.

Is b in W? How many vectors are in W?

I don't understand how this any different than part a because

b=[4;1;-4] and W=Span{a_1,a_2,a_3}

replacing W and B in the question with this information I get

"Is b=[4;1;-4] in Span{a_1,a_2,a_3}? How many vectors are in Span{a_1,a_2,a_3}?"

which looks just like part a to me

"Is b in {a_1,a_2,a_3}? How many vectors are in {a_1,a_2,a_3}?"

I don't understand how part a and part b are different and I guess what exactly I'm being asked even sense the questions are different some how.

I have no idea what I'm even being asked by

"Show that a_1 is in W. [Hint: Row operations are unnecessary.]"

Thanks for any help. This a question from my home work from my Linear Algebra class, my first class in linear algebra.

See Attachment for Answer from back of book

I do not see how part a and part b are asking me two different things.

I interpret the first part of part a

"Is b in {a_1,a_2,a_3}?"

as

Is b a solution of the system represented by matrix A?

[1,0,-4,4

0,3,-2,1

-2,6,3,-4]

I got up to here

[1,0,-4,4

0,1,-2/3,1/3

0,0,1,-2]

and saw that the system was consistent and stopped and put yes for the first part.

for the second part of part a

"How many vectors are in {a_1,a_2,a_3}?"

I said infinitely many because in the first part of part a I could easily get the matrix in reduced echelon form if I continued and so the fourth column of the matrix could be anything.

For part b.

Is b in W? How many vectors are in W?

I don't understand how this any different than part a because

b=[4;1;-4] and W=Span{a_1,a_2,a_3}

replacing W and B in the question with this information I get

"Is b=[4;1;-4] in Span{a_1,a_2,a_3}? How many vectors are in Span{a_1,a_2,a_3}?"

which looks just like part a to me

"Is b in {a_1,a_2,a_3}? How many vectors are in {a_1,a_2,a_3}?"

I don't understand how part a and part b are different and I guess what exactly I'm being asked even sense the questions are different some how.

I have no idea what I'm even being asked by

"Show that a_1 is in W. [Hint: Row operations are unnecessary.]"

Thanks for any help. This a question from my home work from my Linear Algebra class, my first class in linear algebra.