Find all x in R4 that are mapped into the zero vector by the transformation x-Ax for the given matrix A. 1 -5 18 -9 A = 0 1-5 3 416 52-24 Select the correct choice below and fill in the answer box(es) to complete your choice. OA. There is only one vector, which is x = OB. C. X3 (...) X4

Find the inverse of the matrix if it exists. 8 96 1 -2 4 8 8 7 ↓ 1

Determine whether the statement below is true or false. Justify the answer. If A is an mxn matrix, then the range of the transformation x→Ax is Rm. Choose the correct answer below. O A. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the columns of A. OB. The statement is false. The range of the transformation is R" because the domain of the transformation is RM OC. The statement is true. The range of the transformation is RM, because each vector in RM is a linear combination of the rows of A. O D. The statement is false. The range of the transformation is the set of all linear combinations of the columns of A, because each image of the transformation is of the form Ax.

In the rest of this exercise set and in those to follow, you should assume that each matrix expression is defined. That is, the sizes of the matrices (and vectors) involved "match" appropriately. 3. Let A = 4 5 -2 Compute 312 – A and (31₂) A.