LINEAR ALGEBRA TOP STUDY GUIDE COMPREHENSIVE STUDY SHEET 2026 SOLVED QUESTIONS PREMIUM BUNDLE

LINEAR ALGEBRA TOP STUDY GUIDE
COMPREHENSIVE STUDY SHEET 2026 SOLVED
QUESTIONS PREMIUM BUNDLE

◉ Multiplying a linear equation through by zero is an acceptable
elementary row op.
Answer: False


◉ x-y=3
2x-2y=k
The linear system cannot have a unique solution, regardless of the
value of k.
Answer: True


◉ A single linear equation with two or more unknowns must always
have infinitely many solutions.
Answer: True


◉ If the number of equations in a linear system exceeds the number
of unknowns, then the system must be inconsistent.
Answer: False

, ◉ If each equation is consistent linear system is multiplied through
by a constant c, then all solutions to the new system can be obtained
by multiplying solutions from the original system by c.
Answer: False


◉ Elementary row ops permit one equation in a linear system to be
subtracted from another.
Answer: True


◉ If a matrix is in reduced row echelon form, then it is also in row
echelon form.
Answer: True


◉ If an elementary row op is applied to a matrix that is in row
echelon form, the resulting matrix will still be in row echelon form.
Answer: False


◉ Every matrix has a unique row echelon form.
Answer: False


◉ A homogeneous linear system in n unknowns whose
corresponding augmented matrix has a reduced row echelon form
with r leading 1's has n-r free variables.
Answer: True