Suppose A and B are both orthogonally diagonalizable and AB = BA. Explain why AB is also orthogonally diagonalizable.

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

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Q: If A is diagonalizable and B is diagonalizable, must it be true that AB is diagonalizable? Give a…

A: If A is diagonalizable and B is diagonalizable then it is not necessary for AB to be diagonalizable.…

Q: Show that matsix is not 15 diagonalizable A- 2 -3 2.

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Q: Show that the matrix is not diagonalizable.

A: Solve for det(A - λI) = 0

Q: Show that the matrix is not diagonalizable.

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

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Q: IfQ is diagonalizable, then AT also diagonalizable. إختر واحداً:

A: We need to check whether if A is diagonalizable, then A is also diagonalizable.

Q: Determine whether the matrix is orthogonally diagonalizable.

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Q: is not diagonalizable (by similarity) but is condiagonalizable. 4.6.P2 Show that (a) [ (b) [] is…

A: To show: (a) The matix i10i is not diagonalizable but it is condiagonalizable. (b) The matix 1-111…

Q: Prove that if A is invertible and diagonalizable, then A-1 is also diagonalizable.

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Q: Find two examples to demonstrate that if (a-d)2+4bc =0 then A may or may be diagonalizable

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

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Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

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

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

A: We have to find the given vectors are linearly independent or dependent  Here year I am solving…

Q: Determine whether u = is a linear combination of vị and V2

A: Here given that                        u=213 , v1=13  and v2=2-1 Now we determine that u=213 is a…

Q: Suppose that Q is an orthogonal matrix, then OaQ-8 ObQ-2 d 1Q-0

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Q: Suppose (B-C)D=0, where B and C are mxn matrices and D is invertible. Show that B = C.

A: The given matrix equation is B-CD=0 B and C are the matrices of the order m×n while D is the…

Q: Show that if u and v are orthogonal, then || u * v || = || u || || v ||

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Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

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Q: which of the following is the cofactor A13 of matrix?

A: Simply omit that raw and column whose co-factor matrix required and write rest all elements in same…

Q: Rewrite as a matrix-vector product: Зх + 4у — z + w%3D 12 -x + 2y – z +w = 9 2х — Зу + 2z — 4w %3D -…

A: Here we have to rewrite as a matrix-vector product:  3x+4y-z+w=12-x+2y-z+w=92x-3y+2z-4w=-3

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

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Q: Determine by inspection whether the given set of vectors is linearly dependent or independent. Do…

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Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

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Q: Prove that two vectors are linearly dependent if and only if one is a scalar multiple of the other.

A: Let u & v be two vectors in Rn.Suppose that u & v are linearly dependent . then there…

Q: (2) Prove that if a + b and a – b are orthogonal, then a and b have the same magnitude.

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Q: State whether the matrix is diagonalizable or not. 0 0 7 0 O diagonalizable O not diagonalizable

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Q: Find the matrix A representing the reflection about the line L in R² which consists of all scalar…

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Q: Assume that th e product AB makes sense Prove that if the columns of B are linearly dependent, then…

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Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

Q: Show that if the non-zero vectors s(1), s(2),..., s(m) are conjugate to a positive definite matrix…

A: We are given that the non-zero vectors s(1), s(2), ..., s(n) are conjugate to a positive definite…

Q: snip

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

Q: 2rị + 13 T: R' → R?, T 21, 22, 13, L4 ER -12 - 3r4

A: Given  and the standard bases are given by

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

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Q: Define first the scalar product of a row vector a and a column vector b, each having the same number…

A: The given matrices are,

Q: Prove that, if A is similar to B, and B is diagonalizable, then A is diagonalizable.

A: Given that A is similar to B and B is diagonalizable.  To find A is diagonalizable.

Q: State whether the matrix is diagonalizable or not. 0 6 0 0 O diagonalizable O not diagonalizable

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Q: Suppose A=QR, where Q is m×n and R is n× n. Show that if the columns of A are linearly independent,…

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Q: Show that a. A is diagonalizable if (a – d)² + 4bc > 0. b. A is not diagonalizable if (a – d)² + 4bc…

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Q: Suppose A is invertible and orthogonally diagonalizable. Explain why A–1 is also orthogonally…

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Q: Prove that if A is not square, then either the row vectors of A or the column vectors of A form a…

A: Suppose A is an x×y matrix that is not square. Either A has more rows than column (x>y) or more…

Q: Determine whether the set of vectors in M2,2 is linearly independent or linearly dependent.

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

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Q: State whether the matrix is diagonalizable or not. [:] 0 7 0 0 O diagonalizable O not diagonalizable

A: Given matrix is 0700 and now subtract λ from the diagonal elements=0-λ700-λThe determinant is…

Q: If b ≠0, orthogonally diagonalize A

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Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

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Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

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

A: We have to check