d. Is A diagonalizable? Explain your answer.

Q: Evaluate where x; are Cartesian components of a, and x = |æ|.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectors

A: We have to define  (2a - b + 4c, 3a - c, 4b + c) as a linear combination of three nonzero vectors

Q: 1. Explain why (b x c) must be a linear comnbination of b and c. a X

A: We will use properties of cross product of two vectors

Q: b-a then A is diagonalizable. Let A = 0. Select one: O True O False

A:

Q: (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? 2.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Show every vector a in R² can be written as a linear combination of and

A:

Q: AB is orthogonal

A:

Q: Verify the orthogonality p

A: answer is in next step

Q: let (X; Z) v it piece wise comnected ?

A:

Q: Use the scalar triple product to detemine whether the points A(1, 3, 2), B(3.-1.6), C(5, 2, 0), and…

A:

Q: Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, -1, 6), C(5, 2, 0),…

A:

Q: e diagonalizable?

A:

Q: The scalar product 0v is 0.

A:

Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: How do you know if 3 vectors span R^3? Is there any example?

A:

Q: 8. Determine the dot product of u = [7,-4.1] and v = [3.-2.2].

A: Dot product is also known as the scalar product.

Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

Q: In Exercises 1–4, determine if the vectors are linearly indepen- dent. Justify each answer.

A:

Q: Describe the span of the given vectors (a) geometrically and (b) algebraically.

A: Given :           The vectors are 10-1 , -110 , 0-11   To describe the span of the given vectors…

Q: Define the term orthogonal complement.

A:

Q: Give an example of three linearly dependent vectors in R3 such that none of the three is a multiple…

A:

Q: Give example T2 space but not T3 Space

A:

Q: Let v = Does {v1, V2, V3} span R*? Why or why not?

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: State why (u, v) is not an inner product for u = (ui, u:) and v = (v, V2) in R? %3D (u, v) = (u,v;)²…

A: We are given that u,v=u1v12+u2v22 for u=u1,u2 and v=v1,v2 in R2. We know that an inner product must…

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

A:

Q: What is the resulting diagonalized

A: A quadratic form may be diagonalized by the following procedure: Find a variable x such that x2…

Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where needed to give…

A:

Q: 2 A : 10 %3| 0 -1 4

A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

Q: snip

A: Given Orthogonally diagonalize A=abba,If b not equal to zero

Q: Explain the term vector space.

A:

Q: Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, – 1, 6), C(5, 2, 0),…

A:

Q: describe the span of the given vectors a)geometrically b)algebraically

A:

Q: Q) Let A be diagonalizable so that P-1AP = D. Show that A2 must be diagonalizable.

A:

Q: If d is a scalar multiple of b, then ax%. Select one: True False

A:

Q: Does there exist a pair of orthogonal Latin squares of order 54? Explain why or why not?

A:

Q: Let →a=⟨7,−5⟩ and b→=⟨1,3⟩. Compute the dot product. →a X →b=

A: Given a→ = 7,-5 and b→ = 1, 3. We have to compute the dot product a→·b→.

Q: Since it's an if and only if proof, don't you have to prove "if linearly dependent, then scalar…

A:

Q: diagonalize ona %3D

A: Explanation of the solution is given below...

Q: 32) Use the scalar triple product to determine whether the points A(1, 3, 2),  B(3, -1, 6),  C(5, 2,…

A: This question is related to Vectors, we will solve it using given information.

Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

Q: 2 Let a1 = 151. a2 = and let b = -4, for what value of h is b in the plane spanned by a, and a2? h

A: Since you have asked multiple questions in a single request, we would be answering only the 1st…

Q: f A E R2x2 is not diagonalizable, then A is not diagonalizable. True or False? Give an example to…

A:

Q: If b ≠0, orthogonally diagonalize A

A:

Q: Let T: M2x2(R) → M2×2(R) be defined by T(A) = A 2 1 1 %3D Is T diagonalizable? Show work and…

A:

Q: Define and give three examples of contravariant and covariant tensors ?

A: The space of real numbers can be defined with dimensions Rn. The properties in this space can be…