4. Let 12 A = 3 4 Find all 2 x 2 matrices a B d in M22(R) such that AB = BA.

Q: 2 Suppose A = is positive semi definite matrix then: a 10 O a. Jal < 20 O b. a <-v20 Oc lal < v20 O…

A: Suppose A=2αα10 is a positive semidefinite matrix then which of the following is correct.

Q: | Given that A and B are similar matrices of size n. Then prove the following. i. |A| = |B| ii. AT…

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Q: 2 Let U = { A E M55 : A| 3 ,where M55 is the set of 5 x 5 4 5 matrices. Then dim U O 10. O 15. 5.…

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Q: Suppose A is a 4 x 5 matrix with rank 4. Wha А? O Col (A) = R+ O Nothing O Col (A) # R O Col (A) =…

A: We cannot say anything about it. Since we do not know anything about its determinant. We just know…

Q: 3 1 come up with two matrices D and C such that DA CA but D (b) For A C. 6 2

A: The given matric,

Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Show that AB and BA are not equal for the given matrices.

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Q: Let M, N and K be matrices of type 3 x 2, 2 x 3 and 3 x 3 respectively, such that det(MN) = 2 and…

A: Determinant properties help to find the determinant of the given matrix. Determinant property for…

Q: Let A and B be two matrices of size 3 x 3 such that det(A) 2 and det(B) 3. Then det(3B- AT) = I| 18…

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Q: **15. Suppose A is an m × n matrix and x e R" satisfies (AA)x = 0. Prove that Ax = 0. (Hint: What is…

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Q: 7 Show that A = 13 and B = 4 2 are similar matrices by finding an invertible matrix P satisfying 2 A…

A: Given,A=7-132-4 abd B=1-2-22Let,P=abcd , and P=ad-bc=nSo, P-1=1nd-b-ca where n=ad-bc=dn-bn-cnan

Q: Suppose A and B are 3x3 matrices with det A = 2 and det B = -3. Find det(2BTA-B).

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: We have given  det(A) = 3 If B is singular matrix  det(B)  = 0 detBT=det(B) =0 So,  det2A-2BT =0…

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Q: 6. The trace of the n x n matrix A, denoted Tr A, is the sum of the entries on the main diagonal: Tr…

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Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: • The Matrix B from 3 × 2 at bj = 1 - is го 1. 2 2. 7 3. -1 4. 1 1 -2 2 3 4

A: concept of matrix  bij=1-i/j , the entries of matrix B is b11,b12,b21,b22,b31,b32

Q: 1. Prove or disprove. a) det(4+ B) = det(4) + det(B) b) det(AB²A') = det B c) (A+ B)(A – B) = A² –…

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. If B is a singular matrix then…

A: Let A and B be two matrices of size 4 x 4

Q: 1. Compute the condition numbers of the following matrices relative to || I. [] [ 3.9 1.6 b. a. 6.8…

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Q: Let A and B be two matrices of size 4 x 4 such that det(A) = 3. %3D If B is a singular matrix then…

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Q: Suppose that A is an n x n matrix and det(A) = 2, det(A +I) = 3, and det(A+2I) = 5. Compute the…

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Q: Let A and B be two matrices of size 3 x3 such that det(A) = -2 and det(B) = 2. Then det(2A 2B") =

A: the solution is following.

Q: Let A and M be n x n matrices. If AM = 31, then M-1 O is equal to (1/3) A is equal to (1/2) A O is…

A:

Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: 27. For any matrices A and B for which the product AB is defined, the (L0-entry of AB equals a bu

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Consider the matrices A = |-1 2 2| and B= -1 1 1 -1 -1 (a) Find AT. (b) Compute A². (c) Calculate…

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Q: Let A and B be two matrices of size 3 x 3 such that det(A) = 2 and det(B) = 3. Then det(3B-'A") =…

A: Solution of question as follow

Q: Let A be a nonsingular 4×4 matrix with det(A¯1) = - 2 Then det(2adj(A)) 1 8 -2 4 -1 8 None -4

A: Use the properties of the matrix to solve the problem.

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: We have to check whether given statement is true or false.

Q: If A, B are 3 x 3 matrices such that det(AB)-1)% = det(adj(A)) = 25. Then det(3A". (B)-') 20 and O…

A: We are given that A and B are 3x3 matrices. We are also given that detAB-1=120 and detadj(A)=25.…

Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A-1B") =…

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Q: if A and B are n X n matrices of rank n, prove that AB has rank n

A: Given: A and B are matrix has rank n. To prove: AB has rank n. Formula used: A'A=I where A is any…

Q: If A, B are 3 x 3 matrices such that det(AB 1) = 12 and det(adj(A)) = 16. Then det(3A". (B)1) %3D

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Q: Let A and B be two matrices of size 3 x 3 such that det(A) = 2 and det(B) = 3. Then det(3B-'A") = O…

A: To find the determinant value of given matrices product.

Q: If A, B are 3 x 3 matrices such that det(AB)-1)= and 20 det(adj(A)) = 25. Then det (3AT. (B)-1) a.…

A:

Q: 1) Compute the indicated matrices if: 2 D = ; 3 2 A = |0 -1 B = L7 a) ЗА + DT b) (B – C)" c) (D –…

A: Since you have asked multiple questions with multiple parts, we will answer the first question. If…

Q: 2 Suppose A = is positive semi definite matrix then: 10 O a. a < -V20 O b. a = ±v20 O c. lal < 20 O…

A:

Q: (8) Let A and B be m x n matrices. Prove that the rank of A + B is less than or equal to the rank of…

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Q: Suppose A is a 5x9 matrix and Rank(A) = 3. Find dim(null(A)-). O 1 3 O 6

A: Given; A is a 5*9 matrix and Rank(A)=3.

Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A- B")%= O…

A: Solution of question as follow

Q: Is it true or false? |A+ B" |=| A" + BT for any nxn matrices A and B. Birini seçin: O Doğru O Yanlış

A: To solve the above question we must know the following determinant property of any square matrix…

Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: Solution

Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: Is it true or false? If A and B nxn matrices |A+B|=| A |+ | B| Birini seçin: O Doğru O Yanlış

A: we have to identify the following is true or false

Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A B"): %3D…

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Q: 7. Prove that there is no 3 x 3 matrix A with 01 1 0 0 1 0 0 0 1 1 0 and A 100 %3D 0 00

A: In this question, concept of matrix is applied. Matrix A matrix is a rectangular array or table in…

Q: 1 Let U = A e M55 : A where M55 is the set of 5 x 5 matrices. Then dim U = 4 O 15. О 25. O 10. O 20.…

A:

Q: Show by counterexample that (AB)−1 ≠ A−1B−1. That is, find two matrices A and B for which (AB) -1 ≠…

A: Let