(d) Determine if the vectors w = [2 1 1] is in the row space of A 1 (e) Determine if the vector a = is in the column space of A 3 (f) Find the Nulity of A 13

Q: [-3 -2 Let A= 0 -6 and b = 14 3 2 6 Determine whether b is in the column space of A.

A: If b is in column space of A then Rank (A:b)=Rank(A).

Q: In linear algebra, the column space and the row space have the same dimension.   (True or False)

A: The given statement, "The column space and the row space have the same dimension".The objective is…

Q: (b) Let P = . Express the product PQ as a linear combination of the columns of P. -1 4

A: let P=1235-14 and Q=7-96 Then we have to find the product of PQ as a linear combination of the…

Q: [-1 -1 21 Let A = = [23] 3 7 Write b as a linear combinations of the columns of A b= a₁t and b a2

A: Given,                A=-12-37, and b=-7-23. To write b as a linear combination of the columns of A.

Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

A:

Q: Give bases for row(A), col(A), and null(A). row(A) col(A) null(A) 2-4 201 2 1 2 1 1-2 3 2 2 000 0000

A:

Q: (b) Let L: M2x2 → M2x2 such that L(A) = At. Find the matrix repre- sentation of L from [L]s,s=

A: Given Given  such that .Find the matrix representation of L from S.

Q: Detecmine if the Columns of the mahix beom a Tutihy answer linearly independent Set

A: The Matrix given to us is 0-853-74-15-41-32

Q: Compute the third row of the product (if it exists) by summing an appropriate linear combination of…

A: To Find : Third row of the Product of given matrices.

Q: Determine whether b is in col( A) and whether w is in row(A)

A:

Q: Determine whether b is in the column space of A. A = 1. -102 5 8-10, b = -3-3 6 3

A:

Q: 1. Find all local maximum point, local minimum point, and the inflection the curve y =x* -8x +6

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Explain why v = ( 1, 0, -1) cannot be a row of A and also in the nullspace.

A:

Q: -1 – 7 -3 (a) Let A = 15 6 Find the second column of A-1 without com- 1 3 puting the other columns.

A: Given,A=-1-7-32156132

Q: Express Ac as a linear combination of the columns of A.

A: Given A=2-34-1235-1-2   C=214

Q: Give bases for row(A), co(A) row (A) K(A) -3 41

A:

Q: if (A|b) is in reduced row echelon form, prove that A is also in reduced row echelon form.

A: (A|b) is the augmented matrix formed by placing elements of matrix B to the right of elements of…

Q: Give bases for row(A), col(A), and null(A). 1 1 -4 0 2 1 1 -1 -5 row (A) col(A) null(A) A =

A:

Q: Use row operations to change the matrix to reduced form. 1 1 1 18 5 6 7 24 1 1 1 18 5 6 7 24

A:

Q: Determine whether w is in row(A),

A: The given matrix is A=11-30211-1-4.

Q: Suppose the second column of B is all zeros.  What can you say about the second column of AB?

A: If the second column of B is all Zeros, then the second column of AB will also be all Zeros.

Q: V2 3 V3 Write w as a linear combination of v,., V4 in two different ways. Don't leave any fields…

A:

Q: [5] as a linear combination of the columns of A = -1 3 10. Write j = 1 4 -5 6

A: Our objective is to write y as liner combination of column vector of A.

Q: Find u•v, V•V, ||u||^2, (u•v)v, and u. (5v). u=(2,0,-3,4), v=(0,5,4,5)

A:

Q: Let A, B and C be invertible n-order square arrays such that A and B switch, A and B are…

A: Let A, B and C be invertible n-order square arrays such that A and B switch, A and B are…

Q: 3 4 10 find -5, 5 If A = and B -2

A:

Q: -2 21 =G B = and C =|-i 1 2 0 4 5 [7 1 Let A 3. Which of the following 4 is the third row of AT B –…

A: