2 -3 -7 5 2 -2 [1 0 -2 1 1 0 2 1 1 -2 -4 3 1 -2 1. 1. -1 A 2 0 -4 2 R 0 0 1 3 1 -5 -7 6 2 -7 0 0 Again you may use, without justification, the fact that R is the reduced echelon form of A. Consider the following five vectors in R4: ai a2 az = a5 |1: as (a) Does ag belong to the span of a1, a2, and a5? If not, explain why not; if so, write ag explicitly as a linear combination of a1, a2, and az. (b) Are a1, a2, and az linearly independent? If so, explain why; if not, provide a nontrivial linear depen- dence relation among a1, a2, and a3.

Q: would the two vectors be (1 1 1 0) and then (0 0 0 1)?

A:

Q: Q5: Determine if the following following sets of vectors are linearly independent. 2 2 (a) -3 (b)…

A: Given below the detailed solution

Q: Determine whether the set of vectors in P, is linearly independent or linearly dependent. S = {-x +…

A:

Q: Let u, v, w be vectors. Which of the followings are meaningless? (Hint: The notation x means cross…

A: Use the actual meaning of vector and dot products.

Q: refer  to  image  below.

A: Lineraly dependentv3={-1/3} v1 +{1/3} v2Explanation:Step 1: Step 2: Step 3: Step 4:

Q: O a Ob 1. Which of the following is a set of linearly independent vectors? a. (1,2,1),(1,2,2),…

A:

Q: ...... 4 -2 9. 8. The value(s) of h which makes the vectors linearly dependent is(are) - 88 because…

A:

Q: 3. Determine which of the pairs of vectors are orthogonal. (a) a = (b) u = (c) y = 8 12 -5 3,0 = -3…

A:

Q: Determine if the vector 2 b -A = 3 5 can be written as a linear combination of the vectors ---- 1…

A:

Q: Given the vectors a = (1, 2, 3) and b = (1, –1,2), what is the dot product a · b · a? 4 14 (7,1, –…

A: a=(1,2,3)  and b=(1,-1,2)a.b.a  is dot product of three vectors

Q: Determine which of the following sets of vectors are linearly independent and which are linearly…

A:

Q: The graph below shows vectors u, v and w. 5- -5 -4 -3 ν 4 3 2 -2 2 3 -1 W -2 -3 -4 -5 Clear All…

A:

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

A:

Q: Refer to the vectors u₁ to ug. 1 --0--0--0--0--0-0-0-0 U4 = -4 = 1 u6= 4 2 = (c) -4 (d) 1 U2 = 1 2…

A:

Q: Select an Answer 1. 3 -9 15 21 1 -3 7 -2 7 -11 -17 Select an Answer 2. -2 -6 -1 -3 1 4 Select an…

A:

Q: In R³ you are given the vectors a = (21,-9, -21,-4) b = (x, -35, -16, -23) Choose a such that b…

A:

Q: Find the best approximation to z by vectors of the form c, v, + C2V2 4 -7 1 1 V2 = 2 z= 3 [-1] 4 1…

A: To find  The best approximation to Z by the vectors of the form c1v1+c2v2.

Q: The cross product (u x v) of the two vectors u = i-2j + k and v = 3i + j - 2k is -3i - 5j7k. True

A:

Q: 1 -3 8. Let vi V2 and v3 = be given vectors in R4. Which of the following vectors is a linear…

A:

Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

A:

Q: a,b are two vectors then ax {ax (a xb)} =? ans. lal (6 xa) lal (a xb)

A:

Q: The following vectors are linearly dependent [4 2 6],[3 -1 2], [10 0 10] Select one: O True O False

A:

Q: Which of the following vectors are linearly independent? 4 2 - 8 108 5 3 - 21 7 -8 -5 All of these C…

A:

Q: b1 bị If 2 b2 then C(A) contains all vectors b2 such that b3 O a. 2b2 = b1 and 3b3 = b1 O b. bz =…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.