Question 19 Suppose that A and B are n x n matrices. If A and B are similar ma OdA= P¹BP. for all invertible matrix P O Statements a, b, cand d O al matrices A and B have the same characteristic polynomial and same ei Statements, and d © Statements a cand d dif A is similar to B. then B is similar to A as well Ob(A) cuals det(B) provided they have the same main diagonal Ⓒ Statements abandd

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Q: b) If P−¹AP and P-¹BP are both diagonal matrices, show that AB = BA.

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Q: Are the following matrices invertible? Choose Choose Choose Choose ✓ 1. v2. v 3. v4. 3 [54] -40 [ 0…

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Q: しt A and B be similar inrertiblo matricen Ghow that and B" are rimilar

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Q: 6. Let A, B, and A+B all be square invertible matrices of the same size. Show -1 that (A+B) = A(A+B)…

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Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

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Q: n If A, B, and C are 2x2 matrices; and det(A) = 5, det(B) = 1, and det(C)=-4 then compute:…

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Q: For matrices A, B, and C, if A is invertible and AB-C, then True False B = CA-¹.

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Q: [0 0 01 10. Let A=100. Show that A³=0. Use matrix algebra to compute the product of Lo 1 ol…

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