questions below:

The vector x is in a subspace H with a basis B ={b1,b2}. Find the B-coordinate vector of x. b1=[-:]2=['1]'x=[13J Explore the effect of an elementary row operation on the determinant of a matrix. State the row operation and describe how it affects the determinant. abc 567 567.abc 342 342 What is the elementary row operation? 0 A. Row 1 is replaced with the sum of rows 1 and 3. O B. Row 1 is replaced with the sum of rows 1 and 2. O C. Rows 1 and 2 are interchanged. O D. Rows 2 and 3 are interchanged. O E. Row 2 is replaced with the sum of rows 2 and 3. O F. Rows 1 and 3 are interchanged. O G. Row 2 is replaced with the sum of rows 1 and 2. How does the row operation affect the determinant? O A. It multiplies the determinant by 2. O B. It increases the determinant by 1. O C. It changes the sign of the determinant. O D. It does not change the determinant. Find the 3 x 3 matrix that produces the described composite 2D transformation below, using homogeneous coordinates. Translate by (4,8), and then rotate 45 about the origin. The 3x 3 matrix is D. (Type an exact answer, using radicals as needed.) Find formulas for X, Y, and Z in terms of A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula. [Hint: Compute the product on the left, and set it equal to the right side.] Find the formulas for X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix. X = Y = Z=