|(1) Show that if A is an n × n symmetric, positive semi-definite matrix, then A must have nonnega- tive diagonal elements. |(ii) Show that if A is an n × n symmetric, positive definite matrix, then A must have strictly positive diagonal elements. (iii) Write down a 2 × 2 symmetric matrix with strictly positive diagonal elements that is not positive definite.

Q: If A and B are symmetric matrices, will A*B*A be symmetric? Please provide proof.

A: Concepts to be used :A matrix Mis said to be symmetric if,MT=M, where MTis the transpose of the…

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Q: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

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Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

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Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

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Q: Show that the inverse of a nonsingular lower triangular matrix is lower triangular.

A: We have to prove that inverse of a nonsingular lower triangular matrix is lower triangular.

Q: ) Let A, B be matrices with real coefficients. (a) Find A and B such that AB is defined and BA is…

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Q: Show that any positive definite square root of a diagonal, positive definite 2 x 2 matrix must also…

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Q: Suppose A is a square matrix. Show (a) A+A" is symmetric, (b) A – A" is skew-symmetric, (c) A= B+ C,…

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Q: (1 b) Write a common matrix with a format (5 x2) form, provide a specific numerical example. Write a…

A: For the solution follow the next step.

Q: Prove that a matrix with a column of zeros cannot have an inverse.

A: Prove that a matrix with a column of zeros cannot have an inverse.

Q: TRUE or FALSE: Every invertible n xn matrix is similar to the identity matrix In.

A: To state true or false given statement.

Q: Explain the rank of a n*n non-singular matrix?

A: Consider Use the property of rank which states

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Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

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Q: a) Use Fermat’s little theorem to compute 3302 mod 5, 3302 mod 7, and 3302 mod 11.b) Use your…

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Q: True or False. Why? An expression of an invertible matrix A as a product of elementary matrices is…

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