1 4 11 5 --:-/- -12-1 Let vi? 0 , V2 and w= 1 -1 4 1 5 7 a. Is w in {V1, V2, V3}? How many vectors are in {V1, V2, V3}?

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1 4 11 5 12 1 Let Vi 0 V2 And W 1 1 4 1 5 7 A Is W In V1 V2 V3 How Many Vectors Are In V1 V2 V3 1 (398.65 KiB) Viewed 25 times

1 4 11 5 --:-/- -12-1 Let vi? 0 , V2 and w= 1 -1 4 1 5 7 a. Is w in {V1, V2, V3}? How many vectors are in {V1, V2, V3}? b. How many vectors are in Span{V1, V2, V3}? c. Is w in the subspace spanned by {V1, V2, V3}? Why? a. Is w in {V1, V2, V3}? O A. Vector w is in {V1, V2, V3} because it is a linear combination of V1, V2, and V3. 1 B. Vector w is in {V1, V2, V3} because the subspace generated by V1, V2, and vz is R3. OC. Vector w is not in {V1, V2, V3} because it is not a linear combination of V1, V2, and V3. 1 D. Vector w is not in {V1, V2, V3} because it is not V1, V2, or V3. 1 How many vectors are in {V1, V2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. , O A. The number of vectors in {V1, V2, V3} is 7 B. There are infinitely many vectors in {V1, V2, V3}. 1 b. How many vectors are in Span{V1, V2, V3}? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The number of vectors in Span{V1, V2, V3} is . B. There are infinitely many vectors in Span{V1, V2, V3}. c. Is w in the subspace spanned by {V1, V2, V3}? 0 b] with b+0. O A. Vector w is in the subspace spanned by {V1, V2, V3} because w is a linear combination of V1, V2, and V3, which can be seen because any echelon form of the augmented matrix of the system has no row of the form [O B. Vector w is not in the subspace spanned by {V1, V2, V3} because the rightmost column of the augmented matrix of the system x7 V1 + x2 V2 + x3 V3 = w is a pivot column. OC. Vector w is in the subspace spanned by {V1, V2, V3} because the subspace generated by V1, V2, and vz is R3. : ។ D. Vector w is not in the subspace spanned by {V1, V2, V3} because w is not a linear combination of V1, V2, and V3.