Consider the matrix A = -8 -2 -9 6 4 8 4 04 and the vector w= 2 1 -2

Compute the product using the methods below. If a product is undefined, explain why. a. The definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights. b. The row-vector rule for computing Ax. A. a. Set up the linear combination of the columns of A using the corresponding entries in x as weights. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O B. + Xgây +Xz&2 + … +xnªn = (x₁ )ª₁ + (x₂)ª₂ + (×3)ª3 = ( C (Type the terms of your expression in the same order as they appear in the original expression.) 8 4 5 53 2 + 1 1 1 X₁ ª₁ +X₂ª₂ + ….. + xnªn = (×₁ )ª₁ + (×₂)ª₂ = (¯ + ( (Type the terms of your expression in the same order as they appear in the original expression.) OC. The matrix-vector Ax is not defined because the number of columns in matrix A does not match the number of entries in the vector x. D. The matrix-vector Ax is not defined because the number of rows in matrix A does…

Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 2 7 V1 1 V2 2 -3 3

Let A = b 6 3 -6 3 0 4 3 1 and b = a₁+ a3= a. Is b in {a₁, a2, a3}? [Select an answer b. How many vectors are in {a₁, a2, a3}? (Enter o for infinitely many.) c. Is b in Span{a₁, a2, a3}? Select an answer d. If b is in Span{a₁, a2, a3}, write b as a linear combination of a₁, a2, a3. Don't write anything if b is not in Span{a₁, a2, a3}. a₂+ -27 -27 a₂+ a3 e. How many vectors are in Span{a₁, a2, a3}? (Enter ∞o for infinitely many.) . Denote the columns of A by a₁1, a2, a3. f. Show that az is in Span{a1, a2, a3} by writing a3 as a linear combination of a1, a2, a3. a₁+ a3