2. Consider the matrices [2 -1 [2 0 D= |1 4 5 4 3 and F= |0 1 1 2 (a) Show that A, B, C, D and F are invertible matrices.

Q: 2. Consider the matrices [3 4 A= 2 -7 -1 8 [3 C = 2 -7 -1 2 -7 1 8 1 5 4 1 B = 2 -7 -1 1 4 1 3 Find…

A: Elementary matrix are obtained from Identity matrix using elementary row operation on Indentity…

Q: 3. If A and B are two matrices of size 4 x 4 such that Det(A) = -3 and Det(B) = , then…

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Q: prove that if A and B are invertible matrices with the same size then AB is also invertible and :…

A: A and B are invertible. So, AB=BA=I

Q: a) Consider the following matrices: 1 0 01 A =| 2 [1 0 01 0 0,B = |o 0 o,C Lo o 1. [o 0 01 2 ,D = |0…

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Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: If any three square matrices have the same size as A ,B,C AB=I and CA=I prove that A=C=A^-1

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Q: (2) Which one of the following matrices is invertible? 21 (a) 10 -1 23 [4 1 -3] 0. -6 1. (е) 2 (c) 1…

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Q: Given that P and O are 3 x 3 invertible matrices then (A-"B) = A. AB-! B. B-'A C. B-'A-! D. BA-

A: Given : A-1B-1

Q: ¯ 3 Determine the dimensions of Nul A and Col A for the matrices. A = 2 -1 -4 -3 4 -3

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Q: If C and D are two n x n invertible matrices, then one of the following is always correct a) (DC)¬l…

A: Use property of matrix

Q: Consider the following 3 x 3 matrix: a -1//2 1/V3 1//2 1//3 c. -1//3 where a, b, c E R. How many 3 x…

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Q: 3. Show that A and B are not similar matrices. [1 A = 0 2 1 -1 Lo 14.8= [2 1 1] 1 0 L2 0 1 ,B= 0

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Q: 7. Consider the following 3 x 3 matrices, [ 1 3 0 -3 2 A -1 1 and В -1 1 0 -3 2 -2 0 -6 Find two…

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Q: Let A and B be 4 x 4 matrices with det(A) = -2 and det(B)=-1. Then det(-2A-B")= %3D

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Q: Which of the following matrices is NOT invertible? 3 5 5 -3 7 4 0 0 ( 2 4 1 3 3 2 4 1 4. 1 2 3 4 0 4…

A: We have to check which of the following matric is not invertible. Invertible matrix:- A matrix is…

Q: Show that the matrices [1 1 1] A = |1 3 0 and B = |0 o 0 0 1 1 1 1 are similar.

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Q: 6. For any two nx n non-singular matrices A and B, then (a) K(A. B) ≥ K(A). K(B) (c) K(A. B) K(A).…

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Q: If B and C are all invertible n x n matrices, then BC-l is the inverse of BC. O True O False

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Q: For all invertible matrices A and B, (AB)= AB1 O True O False

A: This can be solved as follows:

Q: If A and B are matrices such that AB is defined, then it is true that (AB)T = ATBT %3D True False

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Q: 1) Classify the following matrices into singular and non-singular matrices 2 4 3 a) 3 b)|-2 -4 -3 -2…

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Q: Let A, B, and C be invertible matrices. Then (4BT A-1C²)-1 is equal to None of the mentioned equal…

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Q: Suppose that A and B are invertible n x n matrices. Which of the following statements is true. A.…

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Q: Show that AB and BA are not equal for the given matrices. 1 1 1 1 5 2 2 2 A = B = 1 1 1 1 2 5 АВ ВА

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Q: Suppose A , B and X are matrices such that AX - A = B, where 1 -1 3 4 1 20 4 5 6 -5 1 2 1 -2 1 A = 3…

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Q: 3. The following matrices are elementary matrices except (a) 1 0 1 0 (b) 5 1 (3 (c) 1 (d) -3 -

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Q: 4. Suppose B, I – B-' are invertible matrices and (X – A)- = BX-1, find X (as an expression in A,…

A: A matrix Y is said to be invertible if and only if Y-1 Y=Y Y-1=I

Q: If AB=AC, where A, B, and C are matrices, then this implies that B=C. O True O False

A: A-1A = A A-1 = I  Where A-1 = Inverse of A               I = Identity matrix

Q: Given that A- -3 -1 -5 2 has the form A = PCP-¹. O P= O 2 -1 1 0 2 and P= O and C= Find an…

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Q: Let A and B be n x n matrices. If AB = [0], then BA = [0]. A True False

A: Solution

Q: If A and B are square matrices of the same size such that det (A) = det(B), then det(A+ B) =…

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Q: 13. a) Show that if A and B are n x n matrices, at least one of which is invertible, then AB and BA…

A: (a) If A and B are two n×n matrices, and one of them is invertible, then show that AB and BA are…

Q: Example 1: For the matrices A = 0. and B= compute AB andA-1 and B-1 and (AB)-1.

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Q: Given the matrices below and that A = LU, complete L-1,U-1,and A-1 1 0 0 L = |1 1 1 4 -1 1 4 A = 1…

A: Given that A=14-115-6213-26 and A=LU where L=100110251 and U=14-101-5001

Q: If A and C are non-singular matrices, then show that A 0 A-1 C-BA-1 C1 1 0 0 0 0 2 0 0 3 0 4 0 1 0 3…

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Q: . If A and C are non-singular matrices, then show that A-1 - C-'BA¬1 C A 0 B C 1 Hence find inverse…

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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: 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: . If A and C are non-singular matrices, then show that A 0 A-1 В С, - C-'BA-1 C1 0 0 0 0 2 0 0 3 0 4…

A: To show the below statement if A and C are non-singular matrices. AOBC−1=A−1O−C−1BA−1C−1 To find the…

Q: 6. Show that (AA)* = X* A* for all A E C and all matrices A.

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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(2A- B")%= O…

A: Solution of question as follow

Q: 5. Find three 2 x 2 nonzero matrices A, B and C such that B C and AB = AC = 0.

A: To find the matrices A, B and C satisfying the given conditions.

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: Which of the following matrices is singular? O a. -1 0 3 1 4 -4 2 2 O b. 1 2 3 1 1 -1 2 22 Oc/-1 3…

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Q: -4 Let A = Find a matrix B such that AB=I. 1 - 1 1 O a) 4 O b) 1 1 4 3. c) - 3. 3 1 4 3. o d) 3. 4…

A: To find a matrix B such that AB=I

Q: One of the following matrices is not invertible 4 2 9 1 0 03 7 4 1 a) 0 0 54 b) 5 6 0 0 0 6 2777 40…

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Q: If A, B are 2 × 2 matrices such that AB = 0 then BA= 0. | O true O false

A: Please refer to the image below.

Q: 6. For any two nx n non-singular matrices A and B, then (a) K(A. B) ≥ K(A). K(B) (c) K(A. B) K(A).…

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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 O…

A: Consider the given expression, det3AT·B-1 It is given that detAB-1=12 and detadjA=16. now, use the…