Question 11*: Using the Caley-Hamilton Theorem, compute the inverse, A and e" for cach the following matrices. -28 18 -6 15 -9 -18 A, -78 48 -14, A, = -90 42 90 54 -27 -57 -69 39 -7

Q: 1. How would you verify that matrix A1 is the inverse of matrix A?

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Q: Consider the matrices A = B = 2 3 (²7¹) and (-18 -1), ₁ 3 (₁1).If A - zB = Select one: O a. 5 O b. 4…

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Q: Show that matrices A and B = are inverses of each 2 3 other.

A: See the details solution in below

Q: Find the inverses of the matrices or show that they do not exist. -5 -3 1 -2 A B= = 1 6 = 2 -3

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Q: Question 11 Determine the rank of the matrix. 1-2 2-3] 2-47-2 -3 6-6 9] 04 3 01 02

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Q: -1 Consider the matrices A = 4. B = -1 Compute ((BA)' ) if possible. Type unde fined if you think…

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Q: Let (13). Which of the following matrices is a solution X of the equation O O 4 = (1²₂3) A O and B =…

A: Topic = Matrix

Q: Verify by direct multiplication that the given matrices are inverses of one another. 4 -7 4 2 7 -1

A: GIVEN : A = 1427            A-1 = -7   42-1

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: (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 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: Consider the following two matrices Select one: a. O b. O c. O d. e. both (A) and (B) are in RREF…

A: Given two matrices are , (A) 1-5000  0100  001     ,  (B) 0101-14001    (.) Row reduced echelon form…

Q: Given that -1 2 -2 1 0 -2 A= 1 and C= -3 2 1 1 -1 3

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Q: 4 -1 If A = 3 3 and B = -3 find 1 -1 -2 A ·B, if possible.

A: For the multiplication , the number of column of first matrix must equal to the number of row of…

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

A: solution are given below..

Q: Question3: Suppose that the n × n matrix P has an inverse. Explain for which of the following…

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Q: Determine whether the two matrices are inverses of each other by computing their product. [24] 00…

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Q: Element (1,2) of the inverse of the matrix is

A: Solution: The objective is to find the element (1,2) of the inverse of the matrix

Q: Find the inverse of the following matrix: -7 5 -6 5 -2 3 1 −1 1

A: Given matrix: We have to find the inverse of the given matrix.

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Which of the following matrices are orthogonal? 1 1 1/3 2/3 2/3 -2/3 2/3 -1/3 2/3 1/3 -2/3) 3 4 -4 3

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Q: -2 - Find the inverse of the matrix A = 6. or state that there is no inverse. 4.

A: A necessary condition for the inverse of a matrix that it must be a non-singular matrix.

Q: 2 21 Compute the adjoint matrix and inverse matrix of the following matrix: -1 1 2 1 1 If the…

A: Explanation of the answer is as follows

Q: 1. [3 – 425 ] let A = [3 – 42 5 ] ans.A -[5 4 – 23] %3D - 23

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Q: 8.7.1. Find the singular values of the following matrices: 1 -2 (c) › (_-²-²) -3 6

A: Let be an matrix. Then the singular values of are the square roots of the positive eigenvalues of…

Q: 2. Compute both AB and BA for the following matrices, and observe that AB + BA: -1 [] B= B-[83] and

A: To compute AB and BA for the following matrices, and to observe that .

Q: 4 -1 5 -2 where I is the identity matrix. Let A = Compute 31 – A and (31)A,

A: To compute the following matrix

Q: Which do you find easier? 3 1 (₁ - ( ) -- (3) (a) A = B = -1 1 1₁- (b) A = ()--(²3) B = -2 15 2 2-2

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Q: 2. For the given matrices A find A-¹ if it exists and verify that AA-¹ = A-¹A=I. If A-¹ does not…

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Q: Find the inverse of the matrix 4 -31 6 if it exists. -2 -2 -7 7.

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Q: please answer  all thanks !

A: If you have any questions let me know in comment box thankyou for your question.

Q: Find the inverse of the matrix A, if it exists Show A= 04 -407 030)

A: Here we have to find the inverse of the given matrix.

Q: Find the inverse of the matrix 2 2 2 -3 -3 !

A: Given  A = 122112-3-31

Q: Use the inverse matrices to find (AB)¯¹, (A7)¯¹, and (24)¯¹. 1 1 1 2 2 1 3 1 244 A-1 = (a) -2 1 3 2…

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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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