Linear Algebra and its Applications!!1!GUARANTEED PASS 1!! LATEST
UPDATE 2025
linear equation - (answers)An equation that can be written in the form a1x1 + a2x2 + ... +
anxn = b, where b and the coefficients a1, ..., an are real or complex numbers.
coefficients - (answers)
system of linear equations (linear system) - (answers)A collection of one or more linear
equations involving the same set of variables, say, x1, ... , xn.
solution - (answers)A list (s1, s2, ..., sn) of numbers that makes each equation in the system a
true statement when the values s1, ..., sn are substituted for x1, ..., xn, respectively.
solution set - (answers)The set of all possible solutions of a linear system.
equivalent linear systems - (answers)Linear systems with the same solution set.
consistent linear system - (answers)A system with at least one solution.
inconsistent linear system - (answers)A system with no solutions.
matrix - (answers)A rectangular array of numbers.
coefficient matrix - (answers)A matrix whose entries are the coefficients of a system of linear
equations.
augmented matrix - (answers)A matrix made up of a coefficient matrix for a linear system
and one or more columns to the right.
, size - (answers)Two numbers, written in the form m x n, that specify the number of rows (m)
and columns (n) in the matrix.
m x n matrix - (answers)A matrix with m rows and n columns.
row equivalent - (answers)Two matrices for which there exists a finite sequence of row
operations that transforms one matrix into the other.
leading entry - (answers)The leftmost nonzero entry in a row of a matrix.
echelon matrix - (answers)A rectangular matrix that has three properties: (1) All nonzero
rows above any row of all zeros. (2) Each leading entry of a row is in a column to the right of
the leading entry of the row above it. (3) All entries in a column below a leading entry are
zero.
reduced echelon matrix - (answers)A rectangular matrix in echelon form that has these
additional properties: The leading entry in each nonzero row is 1, and the leading 1 is the
only nonzero entry in its column.
row reduced - (answers)
pivot position - (answers)A position in a matrix A that corresponds to a leading entry in an
echelon form of A.
pivot column - (answers)A column that contains a pivot position.
pivot - (answers)A nonzero number that either is used in a pivot position to create zeros
through row operations or is changed into a leading 1, which in turn is used to create zeros.
forward phase - (answers)The first part of the algorithm that reduces a matrix to echelon
form.
UPDATE 2025
linear equation - (answers)An equation that can be written in the form a1x1 + a2x2 + ... +
anxn = b, where b and the coefficients a1, ..., an are real or complex numbers.
coefficients - (answers)
system of linear equations (linear system) - (answers)A collection of one or more linear
equations involving the same set of variables, say, x1, ... , xn.
solution - (answers)A list (s1, s2, ..., sn) of numbers that makes each equation in the system a
true statement when the values s1, ..., sn are substituted for x1, ..., xn, respectively.
solution set - (answers)The set of all possible solutions of a linear system.
equivalent linear systems - (answers)Linear systems with the same solution set.
consistent linear system - (answers)A system with at least one solution.
inconsistent linear system - (answers)A system with no solutions.
matrix - (answers)A rectangular array of numbers.
coefficient matrix - (answers)A matrix whose entries are the coefficients of a system of linear
equations.
augmented matrix - (answers)A matrix made up of a coefficient matrix for a linear system
and one or more columns to the right.
, size - (answers)Two numbers, written in the form m x n, that specify the number of rows (m)
and columns (n) in the matrix.
m x n matrix - (answers)A matrix with m rows and n columns.
row equivalent - (answers)Two matrices for which there exists a finite sequence of row
operations that transforms one matrix into the other.
leading entry - (answers)The leftmost nonzero entry in a row of a matrix.
echelon matrix - (answers)A rectangular matrix that has three properties: (1) All nonzero
rows above any row of all zeros. (2) Each leading entry of a row is in a column to the right of
the leading entry of the row above it. (3) All entries in a column below a leading entry are
zero.
reduced echelon matrix - (answers)A rectangular matrix in echelon form that has these
additional properties: The leading entry in each nonzero row is 1, and the leading 1 is the
only nonzero entry in its column.
row reduced - (answers)
pivot position - (answers)A position in a matrix A that corresponds to a leading entry in an
echelon form of A.
pivot column - (answers)A column that contains a pivot position.
pivot - (answers)A nonzero number that either is used in a pivot position to create zeros
through row operations or is changed into a leading 1, which in turn is used to create zeros.
forward phase - (answers)The first part of the algorithm that reduces a matrix to echelon
form.
