## Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1 4 −2 1 3 is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0 2346 (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : → which rotates a point about the origin through an angle of radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices and are row equivalent, they have the same reduced echelon form. In general, + ≠ + (assume and are x matrices). If a matrix is symmetric, then so is + “#. A matrix must be a square matrix to be invertible. If $%&’( ≠ 0, then columns of are linearly independent. If an x matrix is equivalent to “#, then )* is also equivalent to “#. If an + x matrix has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If = “, then is invertible.

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