Math 216 Midterm 1 || with 100% Correct Answers

Existence Property correct answers No rows of zeroes / pivots in every row Rank correct answers # of pivots in rref Pivot correct answers First nonzero entry in a row Rref correct answers Increasing number of leading zeroes (ref) All pivots are 1 All other entries in pivot column are zero Free Variable correct answers Any variable in matrix which is not a pivot Uniqueness Property correct answers There are no free variables / Every column has a pivot What is a characteristic of "tall and thin" matrices? correct answers Can't have universal existence What is a characteristic of "short and wide" matrices? correct answers Can't have universal uniqueness Complete set of solutions for a system of equations correct answers Any particular solution + all homogeneous solutions What can you do with a matrix with the uniqueness property correct answers Left cancel What can you do with a matrix with the existence property correct answers Right cancel How do you know something is an inverse correct answers For A, B is the inverse if AB=BA=I If a matrix has an inverse what else do we know correct answers It is invertible and unique and square Nonsingular correct answers Determinant does not equal zero (AB)^-1 correct answers = B^-1A^-1 Symmetric Matrix correct answers A^T=A Determinant in relation to Area/Volume correct answers The determinant is equal to the area / volume or the stretch factor when a value is already given How do you know a function is linear correct answers iff T(ax+by) = aTx + bTy