Determinant and Inverse problem

I need help with the following; a function takes a generic 2×2 matrix as input, and returns two outputs: the determinant and the inverse. Also, if the determinant is zero, the inverse is set to be an empty matrix (value []), or if the determinant is non-zero, then it calculates the inverse. This needs to be done without using det() and inv() functions. Thank you for your time.

[Adam]

What part do you need help with then? I assume you have read up on the definitions of determinant and inverse of a 2*2 matrix?

[Ben]

I know what they both are, just unsure how to code what the det() and inv() functions would do manually. I am a total beginner, I've coded a simple .m file but not much else. Thanks.

[@Johannes]

The determinant of a 2x2 Matrix is a*d-c*b. For the inverse: http://www.mathwords.com/i/inverse_of_a_matrix.htm

Try to implement the functions and if you have errors or problems upload your .m file.

Best regards,

Johannes

[John D'Errico]

This appears to be homework. You won't learn anything by being given the solution. You will learn by trying to write it yourself.

[Ben]

So far I have

A = [2 3; 8 7]

Determinant =(A(1,1)*A(2,2))-(A(1,2)*A(2,1))

and this runs fine in matlab! I'm having real problems getting my head around the manual inverse, my teacher uploaded a video explaining WHAT it is but not HOW to even remotely start coding it.

[Geoff Hayes]

Ben - a link for the algorithm in finding the inverse of a 2x2 matrix was posted in @Johannes' comment. Look at the Shortcut for 2x2 matrices and you should be able to figure out what is missing. (You have the determinant, so half the work is complete.)

[Ben]

Geoff - I have attached my .m file. I don't understand whether I am required to maniuplate individual matrix values using code, but my code works anyway (I hope!). Thanks everyone for your time.

Answer 1

[Jan]

You want to determine the inverse of a 2x2 matrix. So write down the definition paper:

[a, b; c, d] * [ai, bi; ci, di] = [1, 0; 0, 1]

This can be written as 4 equations with 4 unknowns and you can solve this manually. You get e.g.:

inv_A(2,2) = -A(1,2) / (A(1,1) * A(2,2) - A(1,2) * A(2,1))

Perhaps you recognize some parts of this expression?

[Ben]

This is what I have so far!

[Geoff Hayes]

Ben - so using what Jan has provided, how would you modify your code for any 2x2 matrix?

[Ben]

Geoff - I think I sussed it! Many hours later though. Would you mind checking over my code? I did a 3x3 also, very chuffed. I'd also be grateful if you have a tip on how to get rid of the ''ans='' bit at the end -- if I understand correctly it's doing this because of the nature of the variables in the function I defined?

[Geoff Hayes]

Ben - both of your functions have hard-coded matrices and so do not satisfy the requirement to allow generic 2x2 (and presumably 3x3) matrices as input so you must correct this.

Also, in order to suppress output (from within the function) put semi-colons at the end of your line. For the ans that you see when you invoke your function, make sure that you assign the output from your function to two variables and, again, use a semi-colon

 [det, inv] = invanddet2by2(A);

where A is a 2x2 matrix.

[Ben]

Is the 3x3 better? My 2x2 is broken now because I still can't get my head around the diagonal code that I'd have to write for a random 2x2 matrix (when you flip 1,1 and 2,2 and make 1,2 and 2,1 negative)

[Geoff Hayes]

Ben - I don't understand the diagonal code in your 2x2 matrix inverse function which is still hard-coded as

 DiagonalA2by2 = [7 -3; -8 2];

Again, look at the link posted by @Johannes in his comment. It will tell you exactly how to invert a 2x2 matrix that has the form of

 A = [a b
      c d]

where a, b, c, and d are real numbers. Start with that before proceeding to the 3x3 case (which your code still overwrites the input matrix with A3by3 = [1 2 3; 0 4 5; 1 0 6]).