Question

A) Find a matrix representing L with respect to the ordered basis y1, y2, y3. b) For each of the following, write the vector x as a linear combination of y1, y2, and y3 and use the matrix from part (a) to determine L(x): i) x

a. True
b. False

Answer 1

To find the matrix representing L with respect to the ordered basis y1, y2, y3, use the linear transformation L and the coordinates of the basis vectors. To determine L(x), write x as a linear combination of the basis vectors and use the matrix representing L.

Step-by-step explanation:

To find a matrix representing L with respect to the ordered basis y1, y2, y3, we need to know the transformation L and the coordinates of the basis vectors y1, y2, and y3 in the standard basis. Let's assume L is a linear transformation that maps the standard basis vectors e1, e2, e3 to y1, y2, y3 respectively. The matrix representing L with respect to the ordered basis y1, y2, y3 will have the columns as the coordinates of L(e1), L(e2), and L(e3) in the y1, y2, y3 basis.

To determine L(x), where x is a vector written as a linear combination of y1, y2, and y3, you need to express x in terms of the standard basis vectors e1, e2, and e3. Once you have the coordinates of x in the standard basis, you can multiply the matrix representing L by the column vector of x's coordinates to find L(x).

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