Question

Find a basis b1, b2, b3 for IRS such that P is the change-of-coordinates matrix from b1, b2, b3 to the basis a1, a2, a3, what does the change-of-coordinates matrix P essentially represent?

a) Eigenvalues and eigenvectors
b) Inverse matrix operations
c) Linear transformations
d) Matrix addition and subtraction

Answer 1

The change-of-coordinates matrix P essentially represents linear transformations.

Step-by-step explanation:

The change-of-coordinates matrix P essentially represents linear transformations. It describes how the basis vectors b1, b2, b3 are transformed into the basis vectors a1, a2, a3. Each column of the matrix represents the coordinates of one basis vector in the new basis. For example, if P = [a1' a2' a3'], where a1', a2', and a3' are the column vectors of P, then the first column represents the coordinates of b1 in terms of a1, a2, and a3. Therefore, the correct answer is c) Linear transformations.