Solutions Manual – Linear Algebra and
Its Applications, Global Edition (6th
Edition, 2022, Lay)
linear equation - answer-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 - answer-
system of linear equations (linear system) - answer-A collection of one or more linear equations
involving the same set of variables, say, x1, ... , xn.
solution - answer-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 - answer-The set of all possible solutions of a linear system.
equivalent linear systems - answer-Linear systems with the same solution set.
consistent linear system - answer-A system with at least one solution.
inconsistent linear system - answer-A system with no solutions.
matrix - answer-A rectangular array of numbers.
1
, coefficient matrix - answer-A matrix whose entries are the coefficients of a system of linear
equations.
augmented matrix - answer-A matrix made up of a coefficient matrix for a linear system and
one or more columns to the right.
size - answer-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 - answer-A matrix with m rows and n columns.
row equivalent - answer-Two matrices for which there exists a finite sequence of row
operations that transforms one matrix into the other.
leading entry - answer-The leftmost nonzero entry in a row of a matrix.
echelon matrix - answer-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 - answer-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 - answer-
pivot position - answer-A position in a matrix A that corresponds to a leading entry in an
2
Its Applications, Global Edition (6th
Edition, 2022, Lay)
linear equation - answer-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 - answer-
system of linear equations (linear system) - answer-A collection of one or more linear equations
involving the same set of variables, say, x1, ... , xn.
solution - answer-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 - answer-The set of all possible solutions of a linear system.
equivalent linear systems - answer-Linear systems with the same solution set.
consistent linear system - answer-A system with at least one solution.
inconsistent linear system - answer-A system with no solutions.
matrix - answer-A rectangular array of numbers.
1
, coefficient matrix - answer-A matrix whose entries are the coefficients of a system of linear
equations.
augmented matrix - answer-A matrix made up of a coefficient matrix for a linear system and
one or more columns to the right.
size - answer-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 - answer-A matrix with m rows and n columns.
row equivalent - answer-Two matrices for which there exists a finite sequence of row
operations that transforms one matrix into the other.
leading entry - answer-The leftmost nonzero entry in a row of a matrix.
echelon matrix - answer-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 - answer-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 - answer-
pivot position - answer-A position in a matrix A that corresponds to a leading entry in an
2
