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6 Matrix Multiplicatioin Matrix multiplication can be expressed and observed in several ways; we will see a few of them TYPE: A [-2 10; 2 0 1; 8 5 3; 1 2 -3] TYPE: B-[1 5-2; 0 -7 5 1 3-2 ] Enter the following commands. Some will give errors; this is expected TYPE: AB TYPE: BA TYPE: inv(A) TYPE: inv(B) TYPE: inv (A#A') TYPE: inv(A 'A) TyPE: size(A'*A) TYPE: size(A+A') There should have been three errors COMMENT % [an explanation of why the first error occurred] COMMENT: % [an explanation of why the second error occurred] COMMENT: % [an explanation of why the third error occurred] Let A and B be 1 x m and m × n matrices, respectively. Then the matrix product C = A·B exists. There are multiple ways to view matrix multiplication: 1. The element in the ith row and jth column of C, cij, is equal to the dot product of the ith row of A with the jth row of B. That is, T7L ?1 2. The kth column of C is A times the kth column of B. 3. The kth row of C is the kth row of A times B TYPE: C = A * B Find the entry in position (2,3) of the matrix C in two ways TYPE: C(2,3) TYPE: A(2,:) *B(:,3)

Explanation / Answer

The first error will be in line B*A since B is a 3x3 matrix and A is a 4x3 matrix and hence the number of columns of B(3) is not equal to the number of rows of A(4), which is the necessary condition for multiplication of two matrices.

The second error will be in inv(A) since A is not a square matrix and we know that inverse only exists for a non-singular square matrix.

The third error will be in inv(A*A') since (A*A') is a singular matrix (i.e. determinant of A*A' is 0), and hence its inverse doesn't exist since we know that inverse only exists for a non-singular square matrix.

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