Consider the matrix A = Go). Somebody tells you that powers of A (i.e. A, A², A³, etc.) follow the same pattern as powers of i (i, i², i³, etc.). Are they right? Why or why not? (Note that i refers to the square root of –1, not tne identity r atri: The identity matrix is I.)

Q: 2) Perform the following operations on matrices. 9-5 4 (a) 7 3-6 1-5 4 4 3 8 7 -2 -1 9 62 (b)

A:

Q: 1 -2 [23] -2 5 Let A algebra.) and AB [ 7 6 -9 -1 3 Find B. (Hint: Find A-¹ and use matrix

A:

Q: Question 3 (True/False: if it is true, prove it; if it is false, give one counterexample). Let A be…

A:

Q: 4. 1 -₁ 3 Let B= a. 2 -1 Find B¹ using the formula for the inverse of a 2x2 matrix. b. Find the…

A: Inverse of a

Q: Show that if B is an n × n matrix with entries in C and  B3=B then B is diagonalisable. Where C is…

A:

Q: Q2: Let A, B be matrices of size 3x3 such that and AB = A+2I A = -101 21 2 find A, B?

A:

Q: matrix P and a matrix C of the form -21 a -b b ces P and Care mma to separate answers as needed.) no…

A: Let    Given that Eigenvalues of A are 5+2I and 5-2i With corresponding eigenvectors are 2+2i-i And…

Q: Partition the given matrix so that you can apply one of the formulas from the fig , and then…

A: The matrix  is A=011131 -152 The formula of the inverse of the matrix is A-1=1AadjA. Find detA.…

Q: 3-20. Let D and P be the matrices P = 1 1 -1 0 3 1 2 -2 and D = 0 00 −1 0 02 (a) Find P-1. (b) If A…

A:

Q: The coordinates of v relative to the basis C are given by [v]c = P[v]g. C-B" [v]c = P[v]s C+B -72

A:

Q: Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A.…

A:

Q: ii. the missing elements of the adjoint of M, (-11 1 13 adj(M) = -9 an a2 3 a a33) :=

A: A detailed solution is given below

Q: 1 Adjoin I on the right of A, then use row operations to find the inverse A of the given matrix A.…

A: Given that A=5011414101104151 Adjacent Matrix is  [A|I]=50114141011041511000010000100001

Q: Show AB + BA for the indicated matrices. A= 2 3] B = -1

A:

Q: T:R→ R, 上X T2-2x3 C4 VTエA

A: Given that the  transformation :-

Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

A:

Q: a- B-2 3] and Given matrices Find CAB 3

A:

Q: 5) Consider the following matrix: A = 1 2 20 -1 1 030 (i) Compute the adjoint of A. (ii) Use this to…

A:

Q: 1. The matrix J is given by J= a) Show that J² d -b -C $] a [a b]. c d where a+d=-1 and ad-bc=1.

A:

Q: Consider A = -27 4 2-3 4 1 0 -3 1

A: INTRODUCTION Determinants are mathematical objects that can be used to analyze and solve systems of…

Q: An identity matrix is represented by... О а. Нн-1 O b. H-1H О с. Нн-1н

A: If we multiply a matrix by its inverse we get the identity matrix.

Q: 12. Convert the expression to matrix notation: E = B¡j aj bi

A:

Q: 4. The adjoint of the matrix A=1 2 0 3 1 is b. -1 10 0 -15 -2 4 -1 -1 -5 -2 d. Sone of these c. -1

A: A=20-1120311 first, we need to find the minor matrix M1, 1=det2011:  2 M1, 2=det1031:  1 M=1,…

Q: are the two matrices Simi Siari? If So find B=P'AP 20 030 3 00 A=

A: The solution are next step

Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.