Chapter 1
The process of using elementary matrix operations to transform a matrix into an echelon form.
What is row reduction?
The nxn matrix such that its product with any other nxn matrix returns that nxn matrix.
A value for a matrix which, for a 2 by 2 matrix, equals ad - bc.
What is a determinant?
The simplified matrix form where the leftmost nonzero entry for each row is 1 and all other entries are 0.
What is reduced row echelon form?
The matrix such that its product with another matrix equals the identity matrix.
What is an inverse?
The formula for solving a system of linear equations using determinants and replacing one column at a time with the solution vector.
What is Cramer's Rule?
The property of a set of vectors such that the solution to c1v1 + c2v2 + ... + cnvn = 0 is only the trivial solution.
What is linear independence?
The determinant of a non-invertible matrix.
What is 0?
The value for the determinant of a 2 by 2 matrix with first row 1, 0 and second row 0, 5.
What is 5?
The matrix formed by adding another vector to the right of an existing matrix, used for finding the solutions to a system of equations.
What is an augmented matrix?
A transformation T such that T(u+v) = T(u) + T(v), and T(cu) = cT(u).
What are linear transformations?
The value for the determinant of the product of two matrices with determinants 3 and 8.
What is 24?
The property of there existing a single solution to a system of equations.
What is existence and uniqueness?
The matrix factorization method involving lower and upper matrices.
What is LU factorization?
The value for the determinant of the inverse of a 3 by 3 matrix with first row 3, 0, 0; second row 2, 1, 1; and third row 1, 2, 1.
What is -1/3?