number 2 Given the rref([1 2 3 2 4 6 3 6 9]) = [1 0 0 2 0 0 3 0 0]). State a bas

Question

number 2

Given the rref([1 2 3 2 4 6 3 6 9]) = [1 0 0 2 0 0 3 0 0]). State a basis for the vector space v-Span[1 2 3],[2 4 6]= the vectors used to construct the space, v Circle a single 61 from basis set, and explain your answer. State the matrix, A, representing a linear transformation T:R^3 rightarrow R^3, that maps the vectors in R^3 to their (mirror images) with respect to z-axis. Show your work. Given the multiplicative inverse of A = [1 2 3 1 0 1 0 0 1]), A^-1 = [0 1 -1 1/2 -1/2 -1 0 0 1], Consider a linear transformation T defined by the matrix A. State the dimension of the range of T, Explain your answer and circle a single answer.

Explanation / Answer

Let (x, y, z) be a point in R3. The point of reflection with respect to z-axis is given by the point:

. (x, y, -z).

Thus, if A be the transformation matrix, then we must have

A [x y z]T = [x y -z]T.

Since, x, y coordinates remains unchanged therefore, the first two columns of matrix A will be

[1 0 0]T, and [0 1 0]T.

The coordinates of z is transformed to - z, therefore the third column of the matrix A will be

[0 0 -1]T.

Now, you can easily write the matrix A.

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