Solve the following problems :

for the Matrix Resources:

http://resources.codingthematrix.com/

Matrix-vector and vector-matrix multiplication definitions in Python You will write several procedures, each implementing matrix-vector multiplication using a spec ified definition of matrix-vector multiplication or vector-matrix multiplication These procedures can be written and run after you write getitem(M, k) but before you make any other additions to Mat. These procedures must not be designed to exploit sparsity. Your code must not use the matrix-vector and vector-matrix multiplication operations that are a part of Mat. Your code should use procedures mat2rowdict, mat2coldict, rowdict2mat(rowdict), and/or coldict2mat (coldict) from the matutil module. Try reproducing the results below with the procedures you have written: CHAPTER 4. THE MATRIX 265 0 6 5 10 40 80 Problem 4.17.13: Write the procedure lin.comb_mat vec mult (M,v), which multiplies M times v using the linear-combination definition. For this problem, the only operation on v you are allowed is getting the value of an entry using brackets: v[k]. The vector returned must be computed as a linear combination Matrix-vector and vector-matrix multiplication definitions in Python You will write several procedures, each implementing matrix-vector multiplication using a spec ified definition of matrix-vector multiplication or vector-matrix multiplication These procedures can be written and run after you write getitem(M, k) but before you make any other additions to Mat. These procedures must not be designed to exploit sparsity. Your code must not use the matrix-vector and vector-matrix multiplication operations that are a part of Mat. Your code should use procedures mat2rowdict, mat2coldict, rowdict2mat(rowdict), and/or coldict2mat (coldict) from the matutil module. Try reproducing the results below with the procedures you have written: CHAPTER 4. THE MATRIX 265 0 6 5 10 40 80 Problem 4.17.13: Write the procedure lin.comb_mat vec mult (M,v), which multiplies M times v using the linear-combination definition. For this problem, the only operation on v you are allowed is getting the value of an entry using brackets: v[k]. The vector returned must be computed as a linear combination