Suppose u1, ūz and ūz are linearly independent. Let īj = ủ1+ ủ2, 02 = ủ1 + ủ3 and ī3 = ū2 + 2ūz. Prove that 01, īz and īz are linearly independent.

Q: Show that the list of vectors {r + 2, x² + 2, x³ – 3, x4 – x² + 1} is a linearly independent set of…

A:

Q: Show every vector a in R² can be written as a linear combination of and

A:

Q: Suppose T E L(V, W) and v1, ..., Vm is a list of vectors in V such that Tv1,..., Tvm is a linearly…

A:

Q: Two vectors in R- are linearly dependent if and only if they lie on a line through (0,0). Select…

A: It is false.

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

A:

Q: A set of 5 vectors in R6 cannot be linearly independent. True False

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {x2, 1…

A:

Q: 1.2.4 Prove that vectors (1, 1, 1)", (2, 1,0)", (3, 1, 4)", and (1, 2, –2)" are linearly dependent.…

A: Let v1, v2, v3 and v4 are given vectors that is v1=111  ,  v2=210 , v3=314 and v4=12-2 Claim:    v1…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {−2 −…

A: Given set is Consider

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {1 + 3x…

A:

Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

A:

Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {1 +…

A:

Q: 5. Suppose us v and w are linearly independent vectors. Prove that (i) и+у - 2w, и — v — w, и+ w are…

A:

Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

A:

Q: Let u = (-1,0,1), v= (3,2,1) and w= (0,1,2). (b) Prove that the vectors u v and w are linearly…

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

A: As per Bartleby guideline, we have answered only the 1st question. To get the answer of 2nd…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

A: use the  definition of linear independence  definition to check the correct answer.

Q: Show that the vectors 2 -2 2 uj = 2 uz = 3 uz = 7 1 -5 -3 are linearly dependent. Find all r1, x2,…

A:

Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

A:

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

A:

Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {2 − x,…

A:

Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

A:

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

A:

Q: Two vectors in R2 are linearly dependent if and only if they lie on a line through (0,0). Select…

A: We have to check it is true or false  Two vectors in R2 are linearly dependent if and only if they…

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S=(2-x,…

A:

Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

A:

Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

A:

Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

A:

Q: (d) Let A E M3x3(R) and , ij, Z ɛ R* and they are linearly independent. Suppose that we have A = ,…

A:

Q: a. Is S = {v1, V2, V3} linearly independent

A:

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

A:

Q: If there are no vectors in the set S = {a1; a2; a3} from R^3 who is a multiple of one of the other…

A:

Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {2 +…

A:

Q: Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the…

A:

Q: Prove: If ū and v are linearly independent, also au + bü = cũ + dủ, then a=c and b=d. %3D

A: Introduction: Two vectors u and v are linearly independent, if there exist two scalars such that,…

Q: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

A:

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

A:

Q: 4). Determine whether the set of vectors in P, is linearly independent or are linearly dependent {2…

A:

Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: 7. Show that 3-{(; ) ( ) ( )} -1 2 S = 2 1 6 9 is linearly dependent in M22. Write one of the…

A: According to our guidelines I solve only 1 question, so kindly request you to repost the remaining…

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: S is a linearly independent set,then for any x element of , x is not the linear combination of other…

A: Since, using the following definition of linearly dependent of sets-If a set of vectors is linearly…

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

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.