1. Answer the following questions on matrices: (a) Let X be a matrix given by 1 -1 X= -6 0 What is the product matrix (X

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1 Answer The Following Questions On Matrices A Let X Be A Matrix Given By 1 1 X 6 0 What Is The Product Matrix X 1 (61.87 KiB) Viewed 24 times

1. Answer the following questions on matrices: (a) Let X be a matrix given by 1 -1 X= -6 0 What is the product matrix (XXT) and (X"X)? (where, XT is the transpose of the matrix X] (b) Let 0 denote the 2 x 2 (two rows-two columns) null matrix (a null matrix has all its entries as zero). Find a 2 x 2 matrix M all of whose entries are nonzero and MP = 0. How many such matrices are there? Provide a mathematical reasoning for your answer. (c) Consider a linear equation system Ar = b where A is n x n, r is n x 1 and b is n x 1. Assume that det.A #0 and that the first column of A is equal to b. What is the solution to the linear equation system Ar = b? (Give me the solution and a mathematical reason for your answer)