a.) Let u = (2, 4) and v = (−3, 5). Compute u + v. b.) Let u = (2, 4) and k = 7. Compute ku. c.) Let u = (2, 4), v = (−3, 5) and k = 7. Compute k(u + v). d.) Is V a vector space with the stated operations? e.) If V is not a vector space, which property fails to hold?

Q: Verify that this is a vector set check each property(assoctive, etc): Y = (yo, y#) (xo + yo + 1, x#…

A:

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: If p = a₁ + a₁x + a₂x² and q = bo + b₁x + b₂x² are any 2 vectors in P². Defined function: f(p, q) ==…

A:

Q: Let y = and u = Write y as the sum of two orthogonal vectors, y, in the span of u, and y, which is…

A: Solution

Q: 13. Write the reduced echelon form of a 3 x 3 matrix A such that the first two columns of A are…

A: 13. Given that A3-21=000. We have to find a 3×3 matrix Athat has first two columns of A are pivot…

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: 4

A: We are given the following vectors.

Q: Let 8= {b,,b2} and C= {c1.c2} be bases for a vector space V, and suppose b, = -9c, +8c2 and b, = -…

A: Given basis of a vector space V:

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

A: Projection of vector u on vector v is given by  Projv(u) = u.vv2 v Here u = -i+5j+3kv = -i+j-3k…

Q: 6. Let V be a vector space and v1, v2, V3, V4 are vectors in V. Suppose that {v1, v2, V3} are linear…

A:

Q: Let u4 be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. ©…

A:

Q: |Let j and ū = -4 Write j as the sum of two orthogonal vectors, 1 in 9 Span {u} and 72 orthogonal to…

A:

Q: Suppose a matrix A has n rows and m columns. Select the best statement. (The best condition should…

A: (1). According to question, Matrix A has n rows and m columns.

Q: 6. Determine if the vectors à = [−1, 5, 3], b = [−2, 4, 7], and ₹ = [10,7,1] ar are coplanar.

A:

Q: Determine whether the vectors u = (-3,9,6) and v = parallel, (4, –12, –8) are orthogonal, or…

A:

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: 16. For any vectors a, b and c, show that a. (axb) xc lies in the plane of a and b b. (a x b) X c =…

A: Step 1: Reference: Vector Calculus, Vector triple product

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.