By (v1, v2 , V3 , V4) is a basis for the space V and Bw = (w1, w2, w3) is a basis for the space W. The linear 1 1 3 4 transformation T :V → W has matrix 1 2 2 3 with 1 4 0 1 respect to (By, Bw). If -4 -5 1 , [u2]By 1 1 , [u3]B, which 1 1 of (u1, u2, u3) is in Ker(T)? Only u1 O Only u1 and uz O Every one of the vectors is in Ker(T). O Only U1 and U2 O Only U2

Q: Which of the following are a basis for the orthogonal complement of the span of (1,-2, -5, 1)7 and…

A: NOTE: Refresh your page if you can't see any equations. . write both vectors in the matrix

Q: Let a11 a12 a13 A = a21 a22 a23 a31 a32 a33 3 x 3 real matrix and consider it as a linear map A: R³…

A:

Q: The vectors ū1 (2, –3,0), ūz = (1,4, 1), ūz (2, 8, 2), ū4 (1,0, 0) and üs (3, -5, 2) span R² (you…

A:

Q: Let A € Mnxn (R), & be the standard basis for R", and B = {₁,...,n} be another basis for R". If P is…

A: Given, a matrixA∈Mn×n(ℝ). Given, ε as the standard basis ofℝn and  β={v1,v2,...,vn} as another basis…

Q: Consider the bases for M2x2(R) given by a' : and a the stan- dard basis. For the transformation T :…

A:

Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

A:

Q: 3 -51 -1 . Let W = Span Find an orthogonal basis for W.

A:

Q: → Suppose TR³ R³ be a linear bronsformation whose standard matrix has the basis (o 1, 2), (2, 1…

A:

Q: Consider the ordered bases & = {1, t, t²} and B = {1,t— 1,t² — 2t+1} in P2, the vector space of…

A: Since you have posted a multi subparts question according to guildlines I will solve first(a,b,c)…

Q: Let L: R2 R2 be defined by L 4*]-[***] represents the coordinates of v in the standard ordered…

A:

Q: 1 3 -1 - 7 Let P = -3 -5 v = 2 V2 and v3 = 3 . Complete parts (a) and (b). 4 1 5 a. Find a basis…

A: Consider the provided question, According to you we need to solve only part (b).   Given…

Q: 2. For the following transformations, find a basis B such that the matrix representing T is…

A: We will use the definitions.

Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

A:

Q: · Let B = {b¡, b2, b3} be a basis for a vector space V. Find T (3b¡ – 4b2) when T is a linear…

A:

Q: Let b1 = and b = E: {61, 62 is a basis for R?. Let T : R? → R² be a linear transformation such that…

A:

Q: Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's.…

A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

Q: V has bases B = (v1, v2, v3) and B' = (w1,w2, W3). If wi vị + 2v2 + 4v3, wz = 2v1 + 5v2 + 6v3, wz =…

A: Given that, B=(v1,v2,v3),B'=(w1,w2,w3) Given that,…

Q: If V=R\power{3}, and W\index{1} is the xy plane and  let W\index{2} is yz-plane:…

A: Let (a,b,c) be any element of R3, then (a,b,c)=(x,y,0)+(0,y,z)=(x,2y,z) ⇒a=x, b=2y, c=z ⇒a,b,c∈R ⇒…

Q: Write a basis for the Image of the transformation associated to {:}{: x + 4y 2x+8y y The first…

A: The given linear transformation,.The aim is to find the basis of the image of the transformation.

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.