Inverse of a matrix

%Produce a matlab function that takes n x n A matrix and produces an n x n
%matrix B such that AB=BA=I. If A is not invertible, then your function
%should return an empty(0x0) matrix. Name your function "myInv.m"

I am trying to find B, a matrix multiplied on the left of A such that BA=rref(A). I am using RREFbyLeftMult(A) that has been created for us already to get B.

I then check A*B and B*A to see if they all equal to the n*n identity matrix else I return B=zeros(n,n).

My code does not run. Please help me out as I am still learning.

function B =myInv(A)
[n,n]=size(A);
if n==n
    B = RREFbyLeftMult(A);
    p=B*A;
    q=A*B;
    disp(B);
    p==eye(n,n) %check if p is an identity matrix
    q==eye(n,n)
    B=RREFbyLeftMult(A);
    if A=eye(n,n)
        B=zeros(n,n);
    end
end

Answer 1

[Walter Roberson]

if n==n

Under what circumstances could that be false?

p==eye(n,n) %check if p is an identity matrix

You are assuming there is no floating point round-off.

    B = RREFbyLeftMult(A);
    
    B=RREFbyLeftMult(A);

Why are you doing that again? Has A changed? Has the function changed? Does the function use random calculations?

    if A=eye(n,n)

Comparisons require == not =

[Kojo Anim]

function B =myInv(A)
[m,n]=size(A);
if m==n
    B = RREFbyLeftMult(A);
    p=B
    q=A*B;
    disp(B);
    p==eye(m,n) %check if p is an identity matrix
    q==eye(m,n)
else
    B=zeros(m,n);
end
end

This code keeps giving me either an identity matrix or a zero matrix. Kindly help me out.

[Walter Roberson]

We do not have the code for RREFbyLeftMult

[Walter Roberson]

If A is not invertible, then your function
%should return an empty(0x0) matrix.

Notice that when m ~= n you are returning an all-zero matrix instead of an empty matrix.

[Walter Roberson]

tn = tempname();
mkdir(tn);
tf = fullfile(tn, 'RREFbyLeftMult.m');
urlwrite('https://www.mathworks.com/matlabcentral/answers/uploaded_files/749449/RREFbyLeftMult.m', tf);
ls(tf)

/tmp/tp00d7251c_511e_4989_9525_172adb4e2988/RREFbyLeftMult.m

addpath(tn)

myInv([1 2 3; 4 5 -6; -7 8 -9])

Unrecognized function or variable 'FirstNonzeroRow'.

Error in RREFbyLeftMult (line 10)
i=FirstNonzeroRow(A);

Error in solution>myInv (line 13)
B = RREFbyLeftMult(A);

function B =myInv(A)
[m,n]=size(A);
if m==n
    B = RREFbyLeftMult(A);
    p=B
    q=A*B;
    disp(B);
    p==eye(m,n) %check if p is an identity matrix
    q==eye(m,n)
else
    B=zeros(m,n);
end
end

[Walter Roberson]

tn = tempname();
mkdir(tn);
tf = fullfile(tn, 'RREFbyLeftMult.m');
urlwrite('https://www.mathworks.com/matlabcentral/answers/uploaded_files/749449/RREFbyLeftMult.m', tf);
tf = fullfile(tn, 'FirstNonzeroRow.m');
urlwrite('https://www.mathworks.com/matlabcentral/answers/uploaded_files/749459/FirstNonzeroRow.m', tf);

ls(tn)

FirstNonzeroRow.m  RREFbyLeftMult.m

addpath(tn)

myInv([1 2 3; 4 5 -6; -7 8 -9])

Unrecognized function or variable 'BubbleSort'.

Error in RREFbyLeftMult (line 53)
B=BubbleSort(A,pivot);

Error in solution>myInv (line 16)
B = RREFbyLeftMult(A);

function B =myInv(A)
[m,n]=size(A);
if m==n
    B = RREFbyLeftMult(A);
    p=B
    q=A*B;
    disp(B);
    p==eye(m,n) %check if p is an identity matrix
    q==eye(m,n)
else
    B=zeros(m,n);
end
end

Answer 2

[Kojo Anim]

Any help on what I am not getting right in this code?

function B = myInv(A)
[n]=size(A)

i=RREFbyLeftMult(A)

for i==eye(n)
    if B=i
    end
end
B=zeros(A)
end
end

[Walter Roberson]

for i==eye(n)

for is a keyword and cannot be used as a function. You cannot create a function named for and call it using command/function equivalence passing it the character string i==eye(n) as an argument.

When used as a keyword, for must be followed by an unindexed variable, and then a single = and then something which is one of:

• value : value
• value : value : value
• expression

Although value:value and value:value:value would normally be considered expressions, for optimizes them specially... which is an implementation detail.

All of which is to say that you would have had to write

 for i=eye(n)

using = instead of ==

The behaviour of for is to set the variable to each column of the values in turn. So the first iteration, the variable would be assigned the first column of eye(n), the second iteration the variable would be assigned the second column of eye(n), and so on.

   if B=i

if is also a keyword. It must be followed by an expression, not by an assignment. The comparison operator is "==" not "=" . So you would have had to write

   if B==i

However... no value has been assigned to B at this point in the code.

Is it really the case that you are going to want to compare the vector B to the columns of the identity matrix?

[Kojo Anim]

I want B to be that inverse I am looking for in case the reduced row echelon form of A is an identity matrix

[Walter Roberson]

Then you need to calculate values and assign them to B, rather than testing the value of B that is not even assigned yet.