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3. Matrices A matrix is a rectangular grid of numbers organized into rows and columns Matrices are an important tool in algebra and are often used to solve systems of linear equations. Below are ex- amples of a couple of 2 x 2 matrices (matrices with 2 rows and 2 columns) that we will call M and N M= N N=(: :) (a) A special value associated with any 2 x 2 matrix is the determinant. Given a generic 2 x 2 matrix, the determinant can be computed using the following formula: det ad-bc Using the formula, we can compute the determinant of matrix Mabove as (2/12)-(-4X-6)= 0. Write a Scheme procedure, named (det2x2 a b c d) to compute the determinant of a generic 2 x 2 matrix. Assume that the matrix elements a, b, c and d are given as four formal parameters, Compute the determinant of N. (b) Amatrix is called invertible if its determinant is non-zero. Write a procedure, named (invertible? a b c d), that checks whether or not a generic 2 x 2 matrix is invertible. Verify that N is invertible and M is not invertible. (c) A powerful property of matrices is that certain kinds of matrices may be meaningfully mul tiplied together to get another matrix. It turns out that matrix multiplication is intimately related to composition of linear functions, but you won't need this interpretation to com plete the exercise. In particular, it is possible to multiply 2 x 2 matrices. Assume we have two matrices ab 4 B la de The product of these matrices is defined to be 4,22 + b 2 a by+hd 4-B 942+d6 b + dd) Given two 2 x 2 matrices, we wish to determine whether or not their product A B will be invertible. There are two ways to do this i. Compute the product, as described above, then compute its determinant. Define a function named (prod-inv-direct? al bi ci di a2 b2 c2 d2) which deter- mines if the product of two matrices is invertible by this method. il. It is a remarkable fact that for two matrices A and B. det(AB) = det(A)x det(B). Thus, we can compute the determinant of AB indirectly (without computing the product of the two matrices) from the determinants of A and B. Define a function named (prod-inv-indirect? al bi ci di a2 b2 c2 d2) which determines ifthe prod- uct of two matrices is invertible by this method