UMD MATH240 Exam #1 with all Correct & 100%
Verified Answers| Guaranteed to Pass
Matrix ✔Correct Answer--A rectangular arrangement of values with m rows and n columns.
Column Vector ✔Correct Answer--A single column matrix (1 x N) that defines a vector.
Consistent ✔Correct Answer--A linear system that has at least 1 solution.
Inconsistent ✔Correct Answer--A linear system that has 0 solutions.
Augmented Matrix ✔Correct Answer--A matrix including the coefficients and solutions of a linear
system.
Row Replacement ✔Correct Answer--Replace one row with the sum of itself and a multiple of
another row.
Row Interchange ✔Correct Answer--Swap the order of 2 rows.
Row Scaling ✔Correct Answer--Multiply the entries in a row by a constant scalar
Row Echelon Form (REF) ✔Correct Answer--Matrix with the properties:
- All nonzero entries are above zero rows.
- Each pivot is in a column to the right of the leading entry above it.
- All entries in a column below a pivot are 0.
Reduced Row Echelon Form (RREF) ✔Correct Answer--REF Matrix with the properties:
- Each pivot has the value 1.
- Each pivot is the only nonzero entry in its column.
Basic Variable ✔Correct Answer--A column with a pivot.
Free Variable ✔Correct Answer--A column without a pivot. Matrices with these have infinitely
many solutions if they are consistent.
Vector Addition ✔Correct Answer--Vectors with the same number of rows can be added entry-by-
entry
Scalar Multiplication ✔Correct Answer--All entries in a vector are multiplied by a constant scalar
Linear Combination ✔Correct Answer--A sum of scalar multiples of vectors.
Span (of a set of vectors) ✔Correct Answer--Set of all linear combinations of the set.
Matrix-Vector Product ✔Correct Answer--For a matrix A with n columns and vector x with n rows,
the resultant vector is the linear combination of each column in A scaled by the same row in x.
Row-Vector Rule ✔Correct Answer--The i-th entry of Ax is the sum of the products of i-th row of A
and all of x.
Verified Answers| Guaranteed to Pass
Matrix ✔Correct Answer--A rectangular arrangement of values with m rows and n columns.
Column Vector ✔Correct Answer--A single column matrix (1 x N) that defines a vector.
Consistent ✔Correct Answer--A linear system that has at least 1 solution.
Inconsistent ✔Correct Answer--A linear system that has 0 solutions.
Augmented Matrix ✔Correct Answer--A matrix including the coefficients and solutions of a linear
system.
Row Replacement ✔Correct Answer--Replace one row with the sum of itself and a multiple of
another row.
Row Interchange ✔Correct Answer--Swap the order of 2 rows.
Row Scaling ✔Correct Answer--Multiply the entries in a row by a constant scalar
Row Echelon Form (REF) ✔Correct Answer--Matrix with the properties:
- All nonzero entries are above zero rows.
- Each pivot is in a column to the right of the leading entry above it.
- All entries in a column below a pivot are 0.
Reduced Row Echelon Form (RREF) ✔Correct Answer--REF Matrix with the properties:
- Each pivot has the value 1.
- Each pivot is the only nonzero entry in its column.
Basic Variable ✔Correct Answer--A column with a pivot.
Free Variable ✔Correct Answer--A column without a pivot. Matrices with these have infinitely
many solutions if they are consistent.
Vector Addition ✔Correct Answer--Vectors with the same number of rows can be added entry-by-
entry
Scalar Multiplication ✔Correct Answer--All entries in a vector are multiplied by a constant scalar
Linear Combination ✔Correct Answer--A sum of scalar multiples of vectors.
Span (of a set of vectors) ✔Correct Answer--Set of all linear combinations of the set.
Matrix-Vector Product ✔Correct Answer--For a matrix A with n columns and vector x with n rows,
the resultant vector is the linear combination of each column in A scaled by the same row in x.
Row-Vector Rule ✔Correct Answer--The i-th entry of Ax is the sum of the products of i-th row of A
and all of x.
