If A and B are arbitrary real m × n matrices, then the mapping (А, В) trace(A" в) efines an inner product in IR"X". Use this inner product to find (A, B), the norms ||A|| and ||B||, and the angle a 4.B between A and B for 3 -3 1 -3 A = -3 3 and B= -2 -1 1

Q: Find a basis for the space of 2 × 2 lower triangular matrices. Basis =

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Q: In linear algebra, if a vector is in the range of a matrix A, then it is also in the null space of…

A: The given statement is False.

Q: 5) Give an example of matrices D and F where DF is defined, but FD is not, and clearly explain why…

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Q: 0 5 Let A= 4. diagonalizable matrix( A-XDX), then X and D are: 1 Select one: a. -5 X= -5 0 4 0. b.…

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Q: Show that the inverse of an invertible lower triangular matrix is lower triangular

A: Given : The matrix A is an invertible lower triangular matrix Then we have to show that A-1 is…

Q: If A is an invertible matrix, explain why A and AT must have the same null space. Is this true if A…

A: If A is invertible matrix then it has trivial null space and a matrix is invertible iff AT is…

Q: If the RREF of All is || B, then AB is the identity matrix. A) True B False

A: Given: The row reduces echelon form is A:I is I:B. We have to check whether AB is the identity…

Q: Prove that a 2×2 matrix transforms any straight line into a second straight line and points on the…

A: Let T be a 2x2 matrix given as T = abcd.Let the line be given by y = mx+c.Any point on the line can…

Q: Explain  column vector of m x 1 matrix?

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Suppose A is a 2 × 4 matrix, and B is a 4 × 2 matrix. Assuming that A, B act on vectors in R",…

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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: All elementary matrices are lower triangular matrices Select one: True False

A: The given statement is False. Because we can get elementry matrix by identity matrix by applying the…

Q: What is the multiplicative identity matrix?

A: According to the question, we have to define the multiplicative identity matrix. As the above…

Q: 5. Is the matrix ㅇ 15 아가 Unitary? Explain. 블 ܐ ܥܙܐܡ ܝܐܐ ܙܐ3 춤을

A: A matrix is the arrangement of elements in a row and columns into a rectangular array. The order of…

Q: If Q and U are unitary matrices, show that Q-1 is unitary and also QU is unitary. Start from QHQ = f…

A: As per the question we are given two unitary matrices Q, U and we have to show that Q-1 , QU are…

Q: v that the matrix is invertible and find inverse of the

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Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: If A is a symmetric matrix, does it follow that the transpose of matrix A is also symmetric?…

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Q: Notations That Represent A Line

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Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: determine the diagonalizing matrix: X1 = λαι X2 + X3 = λχη – X2 + X3 = λx3

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Q: 47. Prove that if A and B are square matrices and AB is invertible, then both A and B are…

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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.