Question

Write the matrix equation H=[[58,52],[71,73],[34,-30],[12,-31]],q=[[a],[s]], and m=[[-4],[33],[67],[82]]

Answer 1

To solve the matrix equation Hq = m, we need to perform matrix multiplication and row operations to find the values of a and s.

Step-by-step explanation:

For the given matrix equation:

H=[[58,52],[71,73],[34,-30],[12,-31]],q=[[a],[s]], and m=[[-4],[33],[67],[82]],

To find the solution, we need to perform matrix multiplication:

Hq = m

[[58,52],[71,73],[34,-30],[12,-31]][[a],[s]] = [[-4],[33],[67],[82]]

To solve for q, we can set up the augmented matrix:

[[58,52,-4],[71,73,33],[34,-30,67],[12,-31,82]]

And then perform row operations to reduce the matrix to row echelon form. Using elementary row operations such as multiplying a row by a scalar, adding or subtracting rows, and swapping rows, we can eliminate the values below the main diagonal to obtain the values of a and s.