code in scheme please
(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 complete the exercise.) In particular, it is possible to multiply 2 x 2 matrices. Assume we have two ma- trices: az b2 B = a b A =| C1 C2 The product of these matrices is defined to be (a,a2+ b, C2 Gaz+ d; C2 aj b, + b dz cjbz + dd2 ) A.B =| 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 func- tion named (prod-inv-direct? al b1 c1 d1 a2 b2 c2 d2) which determines if the product of two matrices is invertible by this method. ii. It is a remarkable fact that for two matrices A and B, det(A B)= det(A) x det(B). Thus, we can compute the determinant of A B indirectly (without computing the product of the two matrices) from the determinants of A and B. Define a function named (prod-inv-indirect? a1 b1 c1 di a2 b2 c2 d2) which determines if the prod- uct of two matrices is invertible by this method. Once you have finished: 1. Save your work (the definitions) to a file named lab1.rkt 2. Submit your lab solutions for grading via Mimir. 3. If you haven't already, read the Honor Code Pledge on the CSE1729 Moodle site completely. 4. If you haven't already, hand in your signed Honor Code Pledge in lab today. Please note: assignments will not be graded for credit until your Honor Code Agreement is filed-see it under Course Content in Moodle. (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 complete the exercise.) In particular, it is possible to multiply 2 x 2 matrices. Assume we have two ma- trices: az b2 B = a b A =| C1 C2 The product of these matrices is defined to be (a,a2+ b, C2 Gaz+ d; C2 aj b, + b dz cjbz + dd2 ) A.B =| 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 func- tion named (prod-inv-direct? al b1 c1 d1 a2 b2 c2 d2) which determines if the product of two matrices is invertible by this method. ii. It is a remarkable fact that for two matrices A and B, det(A B)= det(A) x det(B). Thus, we can compute the determinant of A B indirectly (without computing the product of the two matrices) from the determinants of A and B. Define a function named (prod-inv-indirect? a1 b1 c1 di a2 b2 c2 d2) which determines if the prod- uct of two matrices is invertible by this method. Once you have finished: 1. Save your work (the definitions) to a file named lab1.rkt 2. Submit your lab solutions for grading via Mimir. 3. If you haven't already, read the Honor Code Pledge on the CSE1729 Moodle site completely. 4. If you haven't already, hand in your signed Honor Code Pledge in lab today. Please note: assignments will not be graded for credit until your Honor Code Agreement is filed-see it under Course Content in Moodle
