LINEAR ALGEBRA EXAM #1
QUESTIONS WITH COMPLETE
ANSWERS
consistent - Answer-system with at least 1 solution
inconsistent - Answer-system with no solution
equivalent - Answer-two systems with the exact same solution set
strict triangular form - Answer-an nxn system that in the kth equation the k-1 coefficients
must be zero and the coefficient of xk is not 0
Row Echelon Form - Answer-first non zero entry in each non zero row is a 1
if row k is not all zeros, then the number of leading zeros in row k+1 is > the number of
leading zeros in row k
if there are any rows of all zeros, they are below non zero rows
underdetermined - Answer-system with fewer equations than variables
overdetermined - Answer-system with more equations than variables
lead variable - Answer-a column with a leading 1
free variable - Answer-a column without a leading 1
homogenius solution - Answer-system with right hand side of all zeros, always
consistent
linear combination - Answer-Let a1, a2, ..., an be vectors and let c1, c2, ... cn be
scalars. Then the sum of c1a1+c2a2+...+cnan is a linear combination
Consistency Theorem for Linear Systems - Answer-The system Ax=b is consistent iff b
can be written as a linear combination of the columns of A
identity matrix - Answer-1 if i=j, 0 if i!=j
nonsingular - Answer-there exists a matrix B such that AB=BA=I
multiplicative inverse - Answer-a matrix B, when multiplied to A on either side, gives I,
UNIQUE
Type I Elementary Matrices - Answer-formed by swapping row i and j of I
QUESTIONS WITH COMPLETE
ANSWERS
consistent - Answer-system with at least 1 solution
inconsistent - Answer-system with no solution
equivalent - Answer-two systems with the exact same solution set
strict triangular form - Answer-an nxn system that in the kth equation the k-1 coefficients
must be zero and the coefficient of xk is not 0
Row Echelon Form - Answer-first non zero entry in each non zero row is a 1
if row k is not all zeros, then the number of leading zeros in row k+1 is > the number of
leading zeros in row k
if there are any rows of all zeros, they are below non zero rows
underdetermined - Answer-system with fewer equations than variables
overdetermined - Answer-system with more equations than variables
lead variable - Answer-a column with a leading 1
free variable - Answer-a column without a leading 1
homogenius solution - Answer-system with right hand side of all zeros, always
consistent
linear combination - Answer-Let a1, a2, ..., an be vectors and let c1, c2, ... cn be
scalars. Then the sum of c1a1+c2a2+...+cnan is a linear combination
Consistency Theorem for Linear Systems - Answer-The system Ax=b is consistent iff b
can be written as a linear combination of the columns of A
identity matrix - Answer-1 if i=j, 0 if i!=j
nonsingular - Answer-there exists a matrix B such that AB=BA=I
multiplicative inverse - Answer-a matrix B, when multiplied to A on either side, gives I,
UNIQUE
Type I Elementary Matrices - Answer-formed by swapping row i and j of I
