Im not sure what algorithm I should use and have no idea how to describe them. Thanks

(5) (a) Describe an eicient algorithm for computing the product HA, with H a Householder matrix, and A a general matrix. You may assume that H is not given explicitly, and that, instead, the input on H is the corresponding vector w. (Note: Multiplication of two square matrices of size we requires 0(m3) operations, despite of the fact that the number of entries is only 27712. Your algOrithm should cempute HA with 0(m2) operations, which is best possible, since there are m2 entries in A). (b) Using (a) above, write a short code that e'icz'ently solves a square linear system of equations using QR factorization. Guideline: never compute any Householder matrix; simply save its vector 11]. After all, the only time the Householder matrix does anything, it is being multiplied by a vector or a matrix. (c) Run your algorithm on two examples of your choice. The two matrices you choose should have at least order 5 each, and should be invertible. (d) Estimate the complexity of your algorithm, i.e., the number of operations it uses as a function of the order of the system. Note: if your algorithm is designed correctly, the complexity is determined by the QR factorization itself, and not by the subsequent need to solve the system