Input the matrices using MATLAB to solve A 2 1 3 0 1 1 1 2

Input the matrices, using MATLAB to solve

A = [2 1 3 0 -1 1 1 2 1] and B = [2 0 3 -1 -1 -2 4 3 1] Verify that det(A) det(B) = set(AB) Verify that det(A^T) = det(A) Verify that det(A^-1) = 1/det(A)

Solution

For the given program ;

( i ) Let the given array : A [ 2 0 1 ; 1 -1 2 ; 3 1 1] and input the other argument matrix given as : B [ 2 -1 4 ; 0 -1 3 ; 3 -2 1]

Now define c= det A* det B ;

Now introduce a new variable d = A*B (element by element multiplication 3×3 matrix)

Now value of d;Det (d) = value of Det (A) . Det (B)

{ verified }

( ii ) Similarly define , other element

A= [ 2 0 1 ; 1 -1 2 ; 3 1 1]

From the MATLAB code ; for A transpose

B = A . \'

B = [ 2 1 3 ; 0 -1 1 ; 1 2 1] ;

Det (B) = det (A)

{ verified }

( iii ) syntax : Y = inv(x)

Where X ^ (-1) is equivalent to inv (X).

From the value ;

Where A = X ;

A = [ 2 0 1 ; 1 -1 2; 3 1 1 ]

Y= inv(X)

Hence

Det( Y ) = 1/ Det (A) from above value

{Verified}