10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a non-zero vector that is orthogonal to ỉ = . b) What is the value for ||ū|| if u = ?

Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: 2) Write the vector v as a sum of proj span{.…...} (v) and proj spo span{m} orthogonal set V₁,..., V…

A:

Q: Let W be the set of all vectors of the form ū = H V = [-5s- 2t] 5s + 3t 5s + t . Find vectors ū and…

A: Let S={u,v} be a linear independent set and generate W . Then W=span{u,v} .

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Do question one only

A: (a)…

Q: Let l be a straight line that passes through the origin and is parallel to the vectors…

A:

Q: 6. Vector, scalar or meaningless? Explain. ») (ä - 5) + (7 - E) b) (å x 5) – (¿ x đ) c) dlã x )

A:

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Let v1, V2, V3 and u be vectors in R". If u is orthogonal to each of v1, V2, and v3 then u is…

A:

Q: (a) Find the vector projection of a onto b , that is, find proj, a . (b) Find a vector in the…

A: We can solve the problem problem using concept of vector.

Q: 13) given the vector P = apply 20⁰ at the point T (2,4). Label the vector 21², and the endpoint w…

A: We have given the following information:The vector .Apply the vector  at the point

Q: 4. a) b) Let x = 27 + 3j - k, y = i- j + 4k and Z = −3ỉ + ]. Express the vector x – ỷ – 3ž in terms…

A:

Q: H is the set of all vectors x = X2 in R³ with the property that X3 X1 + x2 = 0 and Xi – x2 + x3 = 0.…

A:

Q: 6) Find two unit vectors that are parallel to the tangent line of f(x) = tan(x) at the point (7,0).

A: Given that f(x)=tanx We have to find two unit vectors that are parallel to the tangent line f(x) at…

Q: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

A:

Q: 150. Determine the real number a such that vectors a = -3i+2j and b = 2i+aj are orthogonal.

A:

Q: Let W be the set of all vectors of the form 111 ū= -3s- 2t 2s+t -s-2t Find vectors u and 7 in R³…

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.