LINEAR ALGEBRA TEST 1 QUESTIONS
WITH CORREC ANSWERS
span - Answer-the set of all linear combinations of a set of vectors
vector space - Answer-the space where linear combinations make sense; a set with two
operations addition and scalar multiplication which satisfy 10 properties
subspace - Answer-the subset that is also a vector space
linear independent - Answer-a set is this if the only solution is a homogenous one
basis - Answer-a sequence of vectors on the vector space that span the space and are
linearly independent
dimension - Answer-the number of elements in the basis
homogeneous linear system - Answer-a system of linear equation who's constants are
zero in each equation
- will have either the trivial or infinite solutions
- swap rows
- scalar multiplication
- add rows - Answer-What are the elementary row operations?
- first nonzero entry in a row is one
- each leading 1 comes in a column to the right of the leading 1s in rows above it
- all rows of 0s come at the bottom of the matrix
- if a column contains at leading 1, them all other entries in the column are 0 - Answer-
How do you do reduced row echelon from?
-the first non-zero element in each row, called the leading entry, is 1.
-each leading entry is in a column to the right of the leading entry in the previous row.
-Rows with all zero elements, if any, are below rows having a non-zero element. -
Answer-Steps for row echelon from
pivot positions - Answer-a location in a matrix A that corresponds to a leading 1 in the
ref of A
pivot columns - Answer-column of A that contains a pivot
leading variables - Answer-left most nonzero entry in a nonzero
free variables - Answer-all other variables which are not the leading variables
WITH CORREC ANSWERS
span - Answer-the set of all linear combinations of a set of vectors
vector space - Answer-the space where linear combinations make sense; a set with two
operations addition and scalar multiplication which satisfy 10 properties
subspace - Answer-the subset that is also a vector space
linear independent - Answer-a set is this if the only solution is a homogenous one
basis - Answer-a sequence of vectors on the vector space that span the space and are
linearly independent
dimension - Answer-the number of elements in the basis
homogeneous linear system - Answer-a system of linear equation who's constants are
zero in each equation
- will have either the trivial or infinite solutions
- swap rows
- scalar multiplication
- add rows - Answer-What are the elementary row operations?
- first nonzero entry in a row is one
- each leading 1 comes in a column to the right of the leading 1s in rows above it
- all rows of 0s come at the bottom of the matrix
- if a column contains at leading 1, them all other entries in the column are 0 - Answer-
How do you do reduced row echelon from?
-the first non-zero element in each row, called the leading entry, is 1.
-each leading entry is in a column to the right of the leading entry in the previous row.
-Rows with all zero elements, if any, are below rows having a non-zero element. -
Answer-Steps for row echelon from
pivot positions - Answer-a location in a matrix A that corresponds to a leading 1 in the
ref of A
pivot columns - Answer-column of A that contains a pivot
leading variables - Answer-left most nonzero entry in a nonzero
free variables - Answer-all other variables which are not the leading variables
