Let A, B, C be n x n matrices. Verify that (a) A is similar to A. (b) If A is similar to B and B is similar to C, then A is similar to C.

Q: Suppose A, B, and C are all n x n matrices, then a. A 0 = = -|A| x |C| в с B C A 0 с В 4 n B C Rx C…

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Q: Let A, B be 2 x 2 matrices, C a 3 x 3 matrix and D a 1 × 1 matrix. Find the condition on these…

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Q: If A is an 3× 4 matrix and the nullity of A equals 2, find the rank of A .

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Q: Show that A and B are not similar matrices

A: Given matrix is The characteristic polynomial of matrix A is

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

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Q: Let A, B and C be n x n matrices. Then (2AT + BC)T 2A-CTBT O is equal to the above 2A + CTBT is…

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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: Suppose that A is an m x n matrix and B is an n x m matrix. Then the equation (AB) = ATBT is always…

A: Multiplication Property of transpose : We know that the transpose of a produce of two matrices will…

Q: If A and B are (n x n) matrices, then e"e a) True b) False

A: Any expression written in the form of ex form is known as exponential form. Property of exponential…

Q: Show that AB and BA are not equal for the matrices

A: Given: The matrices are given as, Finding the value of AB by using matrix multiplication,

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: Let A be an n xn matrix and B = A+1, where / is the identity matrix, then it is possible for A and B…

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Q: Let A, B, C, D be n x n matrices, each with non- zero determinant, If ABCD = I, then B-l is

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Q: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

Q: For any two 3 x 3 matrices A and B, we have (А + B)(А — В) — А? — АВ + ВА - В?

A: Given statement: For any two 3×3 matrices A and B, we have

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

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Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

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: If A and B are square matrices of the same order, then (AB)T = AT BT True False

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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: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: If A is an m X n matrix and B is an n x p matrix, matrix. To find in matrix A then AB is defined as…

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Q: If A and B are n x n matrices, and vector v is in the image of both A and B, then i must be in the…

A: True or false.

Q: Determine whether the given matrices are linearly independent.

A: Given: 1234,4321 Let  λ11234+λ24321=0λ1+4λ22λ1+3λ23λ1+2λ24λ1+λ2=0

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

A: Solution

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

A: Matrix multiplication, is not communicative under multiplication.

Q: Show that if A and B are n × n matrices and N(A − B) = Rn then A = B.

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Q: Find three 2 × 2 matrices, A, B, and C such that AB = AC with B = C and A = O.

A: Consider the matrices A=0000,  B=1234  and  C=1234. Clearly, B = C and A = O.

Q: Let A, B, C be n x n matrices. Show that if A is similar to B and B is similar to C, then A is…

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Q: Let A and B be n × n matrices and let C = A − B. Show that if Ax0 = Bx0 and x0 = 0, then C must be…

A: Consider the A and B are n×n matrices and C=A-B. If x0=0, Ax0 =0 and Bx0 =0 are nontrivial…

Q: Let A and B be two n x n matrices. Call A and B simultaneously diagonalizable, if there is a single…

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Q: 2. Let A be a 7 x 5 matrix, and suppose AB is a 7 x 9 matrix for some matrix B. What must the size…

A: We know that matrix multiplication is possible only when number of column of first matrix is equal…

Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: Prove that if A and B are similar matrices and A is nonsingular, then B is also nonsingular and A−1…

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Q: If A and B are nXn matrices, then (AB)²=A²B? A True

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Q: Suppose A and B are NONZERO matrices such that AB = [0]. Then there is no other matrix C such that…

A: Solution

Q: Let A be an n xn matrix and B= A+1, where I is the identity matrix, then it is possible for A and B…

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Q: -0 의 B=[ 1 c=, 이1 1-0 1.where j--T, expres (a) Q3/B: If A = A.B, (b) B. C, (c) C.A and (d) A² in…

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Q: Let A, B , and C be square matrices. Show that(a) A is similar to A.(b) If B is similar to A, then A…

A: A matrix M is said to be similar to a matrix N is there exists a nonsingular matrix P such that…

Q: If A and B are nxn matrices, then (AB)²=A²B²_ A) True B) False

A: Solution

Q: Let A, B, C be n × n matrices and assume that A is invertible. Solve the equation A(B + X) = C for…

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Q: Consider an n x p matrix A and a p x m matrix B. If ker(A)-im(B), what can you say about the produet…

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Q: Suppose A and I are bothn x n matrices, then

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Q: Are the two matrices similar? If so, find a matrix P such that B = P-!AP. (If not possible, enter…

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Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

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Q: Show by counterexample that (AB)−1 ≠ A−1B−1. That is, find two matrices A and B for which (AB) -1 ≠…

A: Let

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.