3. Let vi = [1, -2,3], v2 = [-1,–4,5], and v3 = [5,-1,3] be vectors in R³. a) Use determinant to show that v1, v2, and v3 are linearly dependent. b) Use Gauss-Jordan elimination to write Vị as linear combination of v2 and v3.

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: (b) x1 + x2 + 2x3 = 5 + x3 = -2 2x1 + x2 + 3x3 = 3 %3D X1 %3D %3D

A: We see from the given system that, if we add first two equations, we will get the third equation.…

Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors ₁, ₂ in…

A:

Q: Determine if the vectors are Linearly Independent or Linearly Dependent. -2 [1 -5 =|2.X2) = -3 ,x6)…

A: A set of n vectors of length n is linearly independent if the matrix with these vectors as columns…

Q: Express the following system of linear equations as a vector equation. 1x1 +4x2 - 6x3 = -5 -2x1 +…

A:

Q: Three vectors (PQ), (PR), (QR) have been written in matrix form as shown below: 2 -17 PQ1 1 PR = -2…

A:

Q: Express the following system of linear equations as a vector equation. 3 BHOHBHO x2+ 0 7 6 -6 3x₁7x2…

A: To express the following system of linear equations as a vector equation.…

Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

A: Here we have to check whether the given vector b→=745 is linear combination of vectors v1→=1-2-5 and…

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. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

A: Let the given vectors be:w=-7116, u=-112, v=21-5. To Do: We have to write the vector w=-7116 as a…

Q: linearly independent If they are linearly dependent, find scalars that are not all zero s linearly…

A:

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

A:

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

A:

Q: Let W= W= , V1 = , V2 = V3 = If possible, express w as a linear combination of the vectors v₁1, V2…

A:

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

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.