10 -2 Let A = 0 3 -4 and b= 5 . Denote the columns of A by a, , a2, a3, and let W = Span {aq, a2, a3}. -46 2 2 a. Is b in fa,, a2, az}? How many vectors are in {a,, a2, ag}? b. Is b in W? How many vectors are in W? c. Show that a, is in W. [Hint: Row operations are unnecessary.]

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Consider the following vectors: 개 12 람 F= For each of the following vectors, determine whether it is in span{a. 5. 2. If so, express it as a linear combination using a, b, and c as the names of the vectors above -21 -15 -13 -12 -6 163 PPP 7. 입 0 Select an answer >

Let A = 10 - 6 03 - 4 and b = -39 2 11 - 1 - 28 Denote the columns of A by a₁, a2, a3, and let W = Span {a₁, a₂, a3}. a. Is b in {a₁, a₂, a3}? How many vectors are in {a₁, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a2 is in W. [Hint: Row operations are unnecessary.] a. Is b in {a₁, a₂, a3}? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. Yes, b is in {a₁, a2, a3} since b=a (Type a whole number.) B. No, b is not in {a₁, a2, a3} since b is not equal to a₁, a2, or a3. C. Yes, b is in (a₁, a2, a3} since, although b is not equal to a₁, a₂, or a3, it can be expressed as a linear combination of them. In particular, b = (Simplify your answers.) аз. D. No, b is not in {a₁, a2, a3} since it cannot be generated by a linear combination of a₁, a2, and ) a₁ + a₂ + ( ) a3.