Determine whether S = {(1, 1, –3), (–1,2, –3), (4, –1, –2)} is linearly dependent or linearly independent in R. Clearly state and justify your answer. If the vectors are linearly dependent, write one of the vectors as a linear combination of the other two. )-( 1 -1 4 3 0 7 -50 00 1 2 -1 3 -3 -3 -2

Q: The vectors (2, 4, –6), (2, –6, 4) and (4, –2, 10) are linearly Select one: O A. independent O B.…

A: We have to state whether the given vectors are linearly independent.

Q: Civen that 1 00 7 -4 -3 3 2 19 -1 1 4 0 1 0 4 3 -1 4 3 0 0 1 4 3 write 4 as a linear combination of…

A:

Q: Write each vector as a linear combination of the vectors in S. (Use 5₁ and 52, respectively, for the…

A:

Q: (а) (4, — 1, 2), (-4, 10, 2) (Ъ) (—3,0, 4), (5, — 1, 2), (1, 1, 3) (c) (8, – 1, 3), (4,0, 1)

A: As per rules, we will solve first three subparts: a) Given vectors are   u=4,-1,2, v=-4,10,2. To…

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

A:

Q: Which of the following sets of vectors in R° are linearly dependent? Note. Mark all your choices. O…

A: We say a set of vectors v1, v2, ...., vn is linearly independent if…

Q: Eхample: *-? 3 -", -13 2 2. x, =[4 4 -are Determine if the vectors: linearly dependent or not.…

A: The linear dependency of vectors is solved as follows :

Q: The vectors 3 -1 1 i = -3 11 10 + k are linearly independent if and only if k +|

A: We will find out the required value.

Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

A: Set of vectors x1, x2, ...xk is independent vectors if for scalar a1, a2,..., an.…

Q: The vectors 3 -4 3 = 12 w = -8 5 -23 + k 7 are linearly independent if and only if k +

A: Solution:-

Q: #1: a) Express v = (2,13,6) in R³ as a linear combination of the following vectors vị = (1, 5, – 1),…

A:

Q: 2. Consider the vectors =(1,2,3,0),= (0,1,2,3) and = (2,3,4,-3) Let = (1,1,1,1) (a) Is a linear…

A:

Q: D1 = (12, 3, 9) , ô2 = (12, –15, –15), öz = (-8, 16, 18). Are the vectors1.02 and i3 linearly…

A:

Q: 3 3. Let V = 5. Find vectors b₁, 62, 63 such that is a linear combination of b₁, b₂, b3. Additional…

A:

Q: 1 1 -1 |1– 5k + k² 1+4k 1– 2k 3 -2 1

A: we can write the given vectors as a linear combination of vectors…

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.