1. (а) Determine (MN)-1 where M = and N = 4 -5 2 (Ъ) and a · b = a ·c, then it is true that b = c. Can you prove or disprove it? If a, b, and c are three non zero vectors, such that a×a = axc

Q: If vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1) what Is C? Explain.

A: According to question,Given vectors A = (1,2,4) B = (3,4,1) and A+B+C = (3,2,-1)

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: (3) For what value of a the vectors: a = 51 +6j-k and b=2i+(3+a)j- ak A. B = AB cos 90º =…

A:

Q: Find -3w - 6 (u + 2v) if u = -3j, v = i + 2j, and w=--.Express your answer as a linear combination…

A: The given vectors are:u=-3jv=i+2jw=-13i-73j

Q: o) Let v1, v2, V3 be three vectors in F and let W = span {v1, v2, V3}. O What is the largest…

A: Given that v1,v2,v3 be three vectors in F114 and let W=spanv1,v2,v3. (a). Since v1,v2,v3 are three…

Q: 12 2 Determine if the pair of vectors v₁ = 3 V₂ = =-3 are orthogonal. -5 3

A: We have to find whether the given two vectors are orthogonal or not?

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: 1] Determine whether the first vector is a linear combination of the other vectors. (c) (-1, 15);…

A:

Q: Need help with orthogonal vectors.

A: Step 1: Step 2: Step 3: Step 4:

Q: The zero vector 0 = (0, 0, 0) can be written as a linear combination of the vectors V₁, V₂, and v₂…

A: Linear Combination:       A vector V is called a linear combination of vectors   v1, v2, . . ., vn…

Q: 2. (a) (b) (c) Determine if the vectors are linearly independent. Justify your answer. and HNO 8…

A: We use definition of linearly independent vectors.

Q: find the diJ tance betueen the vectors

A:

Q: 2. Express the vector with initial point (1,-1) and terminal point (4,2) as a linear combination of…

A: position vectors

Q: ー0 Let A = -3 -8 %3D そ 14 Label the colmn vectors C ,s,C3, and Cy respeutively. let b. be a linear…

A: The given matrix is ;                     A =  577-10-311-86713914 If  C1 , C2 , C3  and  C4  are…

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Q1: You have the following vectors: U= 6 2 4 V= 3 -2 3 0 3 W = -4 Z- 2 2 2 Which of the vector…

A:

Q: Determine if b is in the span of the other given vectors. If so, express b as a linear combination…

A:

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 15.- Find the…

A: Introduction: Vector Operations are operations that are performed on vector quantities. Vector…

Q: That is not correct. The first Vector answer is [-2/3, -1/3, -2/3] (column wise format.)

A:

Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

A:

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: Determine by inspection the linearly independent vectors !! O a. O b. O C. с. -8 12 4 -2 2 5112]…

A: To determine by inspection the linearly independent vectors.a -812-4, 2-3-1, 000b 51, 28c 4-26, 6-39…

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

A:

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: What is the value of each of the constants that are part of the linear combination between the…

A:

Q: Express the vector b = a₁ + a2 + 2 -4 as a linear combination of the vectors a₁ = a3 = b -2 3 7 , a₂…

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.