f A E R2x2 is not diagonalizable, then A is not diagonalizable. True or False? Give an example to support the assertion

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Let the set {v,, v2} be linearly dependent. Determine whether the set {v, + 4v,, 5v, - v2} is also…

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Q: Prove that (AxB)xC= (A•C)B-(B•C)A. Note that A,B and C are vectors.

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Q: ..... A= -1 1 is diagonalizable. Select one: True False

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Q: If A is invertable then A is diagonalizable. Select one: O True O False

A: If a matrix A of order nxn is invertiable then it has n disctinct eigen values.  And corresponding…

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: Write y as an affine combination of the other points listed. 1 1 5 1 4 - 5 y = -29 %3D V2 V3 2 - 2 1…

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

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Q: Write v as a linear combination of u1, u2, and u3, if possible.v = (0, 5, 3, 0), u1 = (1, 1, 2, 2),…

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Q: O 2 2] B = 0 2 0 0 0 2 TRUE or FALSE: B is diagonalizable.

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Q: For Exercise, use Cramer's rule to solve for the indicated variable. X1 + 2x2 + 3x3 – 4x4 = 3 5x2 +…

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Q: ) Let B = {v₁ =, V₂ =,v3 =}. Determine whether B is linearly independent or linearly dependent.

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Q: Q2: Use vector to check whether the points A (4,3,2), B (4,3,0), C (4,0,0), and D (4,0,2) are…

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Q: If possible, find scalars c1, c2, and c3, not all zero, so that 3. C2 + Cs 2.

A: When any scalar is multiply to a matrix or vector then it will multiplied with all elements of the…

Q: Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject…

A: According to the given information, it is required to find maximum and minimum values and a vector…

Q: Use a graphing utility to determine whether A is orthogonal. 3 |- A = 0 -1 4 3. Find the following.…

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Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

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Q: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

Q: When A is invertible, column of A form a linear dependent set O True O False

A: When A is invertible,column of A form a linear dependent set

Q: Give example T2 space but not T3 Space

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

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Q: Let T : M2(R) → P3(R) be defined by       ( a b) T   (c d ) = dx3 + ax2− bx − c. Determine whether T…

A: Here, the given transformation is: T:M2(R)→P3(R) where Tabcd=dx3+ax2-bx-c

Q: 1. Let 1 1 1 1 -5 0 1 310 A Do the columns of A span R'? Explain.

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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: Let a = ( – 3, 4) and b = ( – 3, 1). %3D | %3D Find the projection of b onto a. projā b %3D

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Q: Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject…

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Q: Write v as a linear combination of u1, u2, and u3, if possible. (Enter your answer in terms of u1,…

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Q: 1. Let A = x 0 Find A20.

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Q: Determine whether v = -2i + 3j, w = -6i - 9j are parallel, orthogonal, or neither.

A: Determine whether v=-2i+3j,  w=-6i-9j are parallel, orthogonal, or neither. Solution:- if two…

Q: When do you use these formulae? Explain briefly. X-X Scaffold 3: X-X a. Z = b. Z = - tion:

A: z score: A z-score represents the number of standard deviations from the mean. It is also called…

Q: Let 2 3 X = X2 = X3 = 6. 3 4 4 (a) Show that x1, X2, and x3 are linearly dependent. (b) Show that x¡…

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Q: Let us say that you are sitting at a coffee shop and you want to impress your significant other by…

A: As per bartleby guidelines for more than three subparts in a question only first three should be…

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

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Q: Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

A: Given: It is given that the quadratic function Q:R2→R such that Q(x)=1 for all vectors x∈R2 such…

Q: Write v as a linear combination of u1, u2, and u3, if possible.v = (−1, 7, 2), u1 = (1, 3, 5), u2 =…

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Q: If possible, find scalars c1, c2, and c3 so that

A: Consider the equation: c112-3+c2-111+c3-14-1=2-23……1

Q: Let a and b be orthogonal such that |ã| = 2 and b = 3. %3D Find (b x a) x ả and |(b × å) × |

A: Given a→=2 and b→=3 We have to find b→×a→×a→   and b→×a→×a→

Q: Let V3 1 A = V2 1 1 V3 1 1 1 V2 V3 If A is orthogonal, what must x equal? Answer:

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Q: Let -81 2 V1 = V2 = 18 23 -2 -3 h For what value of h is y in the span of the vectors v1 and v2? h =

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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: If possible, find scalars c1, c2, and c3, not all zero, so that

A: c112-1+c213-2+c337-4=000c12c1-c1+c23c2-2c2+3c37c3-4c3…

Q: Let u4 be a linear combination of {u1, u2, u3 }. Select the best statement. O A. span{u1, u2, U3} =…

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Q: If b ≠0, orthogonally diagonalize A

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

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Q: Exauple- If v=(T') is a contraviurient vecfor, Shew that He Parhil clenivatokes , dehined in each…

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Q: Write v as a linear combination of u₁, ₂, and u3, if possible. (If not possible, enter IMPOSSIBLE.)…

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Q: Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject…

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Q: Determine whether v = -2i + 3j, w = -6i - 4j are parallel, orthogonal, or neither.

A: Given;                 v=-2i+3j,  w=-6i-4j We say that 2 vectors are orthogonal if they are…

Q: If Q: R" → R is a quadratic form, explain how to determine the maximum and minimum values that Q…

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Q: Let the set {V1, v2} be linearly dependent. Determine whether the set {v, + 4v2, 2v, – v2} is also…

A: The set v1,v2 is linearly dependent. We have to determine whether the set v1+4v2, 2v1-v2 is also…