Science:Math Exam Resources/Courses/MATH152/April 2010/Question A 27

MATH152 April 2010

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Question A 27
Suppose that A is an $8\times 8$ invertible matrix and b is a column vector with 8 entries. Both A and b have been entered into MATLAB. What commands would you use to compute the vector x that solves the linear system $A\mathbf {x} =\mathbf {b} ?$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
What is the special Matlab command for solving a linear system?

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. If we have a linear system $A\mathbf {x} =\mathbf {b}$ then Matlab can solve this via the \ operator. Therefore if we type x=A\b; then the vector x produced by Matlab is the solution to the linear system. (Note that this is not a typo. The command is A\b and not b\A) Note. Since A is invertible, it is possible to get the solution by typing x=inv(A)*b; but you are generally discouraged from using the inv() operation in Matlab to solve linear systems. (That's because calculating the inverse of a matrix A is an overkill here, there is faster ways of finding x that don't require the matrix inverse.)