Let be a 5 times 4 matrix and B be a 4 times 3 matrix. What is the domain of the

Question

Let be a 5 times 4 matrix and B be a 4 times 3 matrix. What is the domain of the transformation defined by B? What is the codomain of the transformation defined by B? What is the domain of the transformation defined by A? What is the codomain of the transformation defined by A? What is the domain of the transformation defined by AB? What is the codomain of the transformation defined by AB? Explain why the product BA is not defined. Ground your explanation in the concepts of composition of functions, domain, and codomain.

Explanation / Answer

If two matrix A and B of order m1xn1 and m2xn2 multiply;

n1 must be = m2;

and resultant matrix is of order m1xn2;

a) B of order 4x3; so Bx is the transformation; x must be a vector R3 -and result is R4;

so domain is R3 and codomain is R4;

b) A of order 5x4; so Ax is the transformation; x must be a vector R4 -and result is R5;

so domain is R4 and codomain is R5;

c)AB matrix is multiplication of 5x4 and 4x3 so result will be 5x3;

AB of order 5x3; so ABx is the transformation; x must be a vector R3 -and result is R5;

so domain is R3 and codomain is R5;

d) since Product BA itself is not defined so the transformation is not defined.

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