4. If A and B are n x n invertible matrices and c ER, prove or disprove the following statements. (a) det (In) = 1 (d) det (A) = det (AT) (b) det (A-¹) = det(A)-¹ (e) det (A + B) = det (A) + det (B) (c) det (A-¹BA) = det (B) (f) det (CA) = [c]" det(A)

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Q: If (X– A)(B – C) = D where all matrices involved are invertible square matrices, then: (A) X = + A В…

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Q: Q3: if it was V2 B =1.A = [VZ o 3] 1.A [V2 O 3) Find В.А A.B , VZB

A: 3B=21-2 ,  A=203B.A=21-23*1 , A= 2031*3=222023121013-22-20-23=2032203-220-6

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A: To find the true statements of matruces

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Q: (i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices,…

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Q: Let A,B,C,D and E denote n x n matrices

A: Step 1:It is provided thatdet(A)=−4det(B)=10det(C)=21​ Let A and B are two matrices and n∈R. Then…

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A: Prove the following (a) Let A and C are symmetric matrices, then . (b)

Q: Let A, B, C be (3 x 3) matrices, such that det(A) = 2, det(B) = 7, det(C) = 1. What is the value of…

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Q: Let A be a 3 x 3 matrix with det(A) = 0. Determine if each of the following statements is true or…

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Q: 6.- For the matrices [A] g 3 -2 4 -2; [A] =-5 3 3 2 3

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Q: Let A and B denote two square matrices. Then answer the following. (a) Prove that a square matrix is…

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Q: Let Ao be an 5 x 5-matrix with det (40) = 3. Compute the determinant of the matrices A1, A2, A3, A4…

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Q: 9. Show that the matrices ( ) ( ) (19). generate M₂×2(F). and (689)

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Q: Let A and B be 3 x 3 matrices such that A 3 = B 6 l10. The matrix C = A – 2B is invertible. [5. (A)…

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Q: [1 3 B = 2 1 5 0 A = 0 -5 4 and 3 8 QA + B'.

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Q: 2. For the matrix A = 2 [1 a) det (A) b) tr (A) c) [1 2 5 Inverse of A 3] 3, calculate 0 81

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