1. Given the vectors x1, X2, X3, X4: a. Determine whether the given set of vectors are linearly independent or not. Show your complete and systematic solution as proof to your answer. b. If it is not independent, express x2 in terms of x1,X3 and x4. Express elements in rational form. (Answers expressed in decimal form will not be accepted) [3] ,X2 1,X3 ,X4 = |7 [2] X1 =

Q: Prove that if a is perpendicular to b, then |a +b|^2 = |a|^2 + |b|^2 .

A:

Q: 9 One requirement can be met while the other fails. Show this by finding (a) A set of vectors in R²…

A:

Q: Select the best statement.

A:

Q: Given Å = £10 – ŷ + 22, B = -& + ŷ10 + 2 and Č = & + ŷ + 210. Vector (Ả x B) x Č is î10 + ŷ10 + 210…

A: To find  (A*B) *C from the given vectors.

Q: -14 Given that write 3 -5 -3 -14 ] -5 = 2 -2 -3 1 0 0 −1 −1 as a linear combination of the vectors 1…

A:

Q: The cross product is not associative. (It is not necessary for | a xb |x c X c to be the x c |.)…

A:

Q: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

A:

Q: Please choose the right answer for the statement below: Suppose V1,V2,V3,V4,V5 are five vectors in…

A: given 5 vectors in ℝ3

Q: Find a general set of solution vectors of х=-5 ха x₁ = x₁ + 3 x ₂ 2 2

A:

Q: a+b = b + a conveys which property of vectors? a. commutative property of addition b. associative…

A: Introduction A vector space (also known as a dimensional space) is a collection of items that may be…

Q: -18 [] 12 Let u= 40 and A= 2-4 9 Is u in the plane in R³ spanned by the columns of A? Why or why…

A: Given : u=-184012   , A=2-4-5922 To Check : A. u is a linear combination of the Columns of A…

Q: Let A = -1 -3 3 and b = b₁ 8} Show that the equation Ax=b does not have a solution for some choices…

A:

Q: 1. Write a statement involving the solutions of a vector equation that's equivalent to each claim:…

A: Sub -Part (1):-  Given information The set of vectors  1-100,  -1100,  05-54,  -38-54,  -217-1512…

Q: Given that 7 write 3 5 7 3 5 -2 2 3 7 -1 2 2 3 3 125 100 010 -5 001 3 as a linear combination of the…

A:

Q: Let a1 0,a22, as a3 2, and b = Write b as a linear combination of a₁, a2, and a3, if possible. b= -1…

A: AssumeThe augmented matrix

Q: give vector form for the solution

A: Here we have to find the vector form

Q: "Given that 3 -4 = 5 -3+ 2 5 ܐ write 3 as a linear combination of the vectors -2 + 5 -3 -2 5 -4 1 2…

A: Here , a vector is given and now we have to represent it as a linear combination of three vectors .

Q: Given that write -4 -2 -5 2 -3 -3 -2 5 3 2 [] -3 as a linear combination of the vectors [100 01 0 0…

A: Given that .We have to write  as a linear combination of the 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.