Homework True or False Flashcards
A linear system whose equations are all homogeneous must be consistent.
True
Multiplying a row of an augmented matrix through by zero is an acceptable elementary
row operation
False
The linear system
π₯ β π¦ = 3
2π₯ β 2π¦ = π
cannot have a unique solution, regardless of the value of π.
True
A single linear equation with two or more unknowns must have infinitely many solutions
True
If the number of equations in a linear system exceeds the number of unknowns, then the
system must be inconsistent.
False
If each equation in a consistent linear system is multiplied through by a constant π, then
all solutions to the new system can be obtained by multiplying solutions from the original
system by π.
False
Elementary row operations permit one row of an augmented matrix to be subtracted from
another.
True
The linear system with corresponding augmented matrix
[
2 β1 4
0 0 β1
]
is consistent.
False
If a matrix is in reduced row echelon form, then it is also in row echelon form.
True
If an elementary row operation is applied to a matrix that is in row echelon form, the
resulting matrix will still be in row echelon form.
False
Every matrix has a unique row echelon form.
False
A homogeneous linear system in n unknowns whose corresponding augmented matrix
has a reduced row echelon form with π leading 1βs has π β π free variables.
True
All leading 1βs in a matrix in row echelon form must occur in different columns.
True
If every column of a matrix in row echelon form has a leading 1, then all entries that are
not leading 1βs are zero.
False
If a homogeneous linear system of π equations in π unknowns has a corresponding
augmented matrix with a reduced row echelon form containing π leading 1βs, then the
linear system has only the trivial solution.
True
If the reduced row echelon form of the augmented matrix for a linear system has a row of
zeros, then the system must have infinitely many solutions.
False
If a linear system has more unknowns than equations, then it must have infinitely many
solutions.
False
The matrix [
1 2 3
4 5 6
] has no main diagonal.
True
For every matrix π΄, it is true that (π΄^π)^π = π΄.
True
For every square matrix π΄, it is true that π‘π(π΄^π) = π‘π(π΄).
True
If π΄ is an π Γ π matrix and π is a scalar, then π‘π(ππ΄) = π π‘π(π΄).
True
If π΄, π΅, and πΆ are matrices of the same size such that π΄ β πΆ = π΅ β πΆ, then π΄ = π΅.
True
An π Γ π matrix has π column vectors and π row vectors.
False
If π΄ and π΅ are 2 Γ 2 matrices, then π΄π΅ = π΅π΄.
False