MATH 136 - WINTER 2019 - UWATERLOO
- THEOREMS AND DEFINITIONS
(addition to the Invertible Matrix Theorem). An n x n matrix is invertible if and only if....... -
correct answer-det A does not equal 0
1)If A is an m x n matrix with m > n, then.....
2)If A is an m x n matrix with m < n, then ....... - correct answer-1) A cannot have a right
inverse
2) A cannot have a left inverse
A set of vectors is linearly dependent if and only if.... - correct answer-
Define
A) Addition and Scalar Multiplication for linear mappings
B) The standard matrices for the above - correct answer-
Define B-coordinates - correct answer-
Define cofactor - correct answer-
Define dimension - correct answer-
Define eigenvalue, eigenvector, and eigenpair - correct answer-
Define k-flat - correct answer-
Define Left and Right Inverses of a Matrix - correct answer-Let A be an m x n matrix . If B is
an n x m matrix such that AB = I, then B is a right inverse of A.
If C is an n x m matrix such that CA=I, then C is called a left inverse of A
Define linearly dependent and linearly independent - correct answer-
Define matrix multiplication. For it to be defined, what must be true in terms of sizes of the
matrices - correct answer-
Define the adjugate of a matrix - correct answer-
Define the B-matrix - correct answer-
Define the change of coordinates matrix - correct answer-
, Define the characteristic polynomial and what must be true for a scalar to be an eigenvalue
of an n x n matrix. - correct answer-
Define the co-factor expansion using rows and using columns - correct answer-
Define the cofactor matrix - correct answer-
Define the composition of linear mappings and the standard matrix for the composition -
correct answer-
Define the determinant of an n x n matrix - correct answer-
Define the following: consistent system, inconsistent system, solution of a system - correct
answer-
Define the range of a linear mapping - correct answer-
Define the standard matrix of a linear mapping - correct answer-
Define upper and lower triangular matrices - correct answer-
Define what a basis is - correct answer-
Define what it means for a function to be a linear mapping - correct answer-
Define what it means for a matrix to be invertible - correct answer-
Define what it means for matrices to be similar - correct answer-
Define what the standard basis is - correct answer-
Define: Linear Combination - correct answer-
Define: Span - correct answer-
Give properties of the cross product - correct answer-
Give properties of the dot product - correct answer-
Give the equation of plane in 3-space two ways - correct answer-
Give the formula for projection/perpendicular onto a line - correct answer-
Give the formula for projection/perpendicular onto a plane - correct answer-
Give the scalar equation of a hyperplane - correct answer-
How does performing row operations on a matrix A affect the determinant? - correct answer-
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