MA 265 Final Exam With Correct
Answers 2025
Any system can be homogenous with the trivial solution -(correct answer)True Fewer
equations that unknowns can never have a solution -(correct answer)False (can have no
solution or infinitely many) A system with linearly independent columns can have a unique
solution -(correct answer)True (A^T)^T = A -(correct answer)True (A+B)^T = A^T + B^T
-(correct answer)True (AB)^T = A^T*B^T -(correct answer)False ((AB)^T = B^T*A^T) r(A)^T =
(rA)^T -(correct answer)True Definition of symmetric -(correct answer)A^T = A Definition of
skew symmetric -(correct answer)A^T = -A (A^-1)^-1 = A -(correct answer)True (AB)^-1 = B^-1
* A^-1 -(correct answer)True (A^-1)^T = (A^T)^-1 -(correct answer)True What method is used
to find the inverse of a matrix by using an augmented matrix? -(correct answer)Gauss-Jordan
How can you solve a linear system (Ax=b) using inverse matrices? -(correct answer)x = A^-1 *
b Difference between REF and RREF -(correct answer)All other entries in columns with
leading ones are 0 Det(A) = det(A^T) -(correct answer)True Effect of swapping rows on
determinant -(correct answer)Changes sign Effect of a zero row/column or equal
rows/columns on determinant -(correct answer)0 Effect of multiplying row/column by k
-(correct answer)Multiplied by k Effect of adding rows or multiples of rows to eachother on
determinant -(correct answer)No change A matrix is invertible if its determinant is 0 -(correct
answer)False (noninvertible) det(AB) = det(A) * det(B) -(correct answer)True det(A^-1) = det(A)
-(correct answer)False (1/det(A)) Ax = 0 has only the trivial solution if det(A) = 0 -(correct
answer)False (has a nontrivial solution if this is true) adj(A): each entry is the corresponding
entry's _____. -(correct answer)Cofactor What is the name of the following process: Ax = b x1
= det(A1)/det(A) etc. where An is the matrix made by deleting the nth column of A with b
-(correct answer)Cramer's rule What is a set of vectors called if: The set spans V Vectors are
liniearly independent All vectors are distinct and nonzero -(correct answer)Basis for V What
does the following process find: RREF the matrix for (av1 +bv2 + cv3 = 0) Take the numbers of
Answers 2025
Any system can be homogenous with the trivial solution -(correct answer)True Fewer
equations that unknowns can never have a solution -(correct answer)False (can have no
solution or infinitely many) A system with linearly independent columns can have a unique
solution -(correct answer)True (A^T)^T = A -(correct answer)True (A+B)^T = A^T + B^T
-(correct answer)True (AB)^T = A^T*B^T -(correct answer)False ((AB)^T = B^T*A^T) r(A)^T =
(rA)^T -(correct answer)True Definition of symmetric -(correct answer)A^T = A Definition of
skew symmetric -(correct answer)A^T = -A (A^-1)^-1 = A -(correct answer)True (AB)^-1 = B^-1
* A^-1 -(correct answer)True (A^-1)^T = (A^T)^-1 -(correct answer)True What method is used
to find the inverse of a matrix by using an augmented matrix? -(correct answer)Gauss-Jordan
How can you solve a linear system (Ax=b) using inverse matrices? -(correct answer)x = A^-1 *
b Difference between REF and RREF -(correct answer)All other entries in columns with
leading ones are 0 Det(A) = det(A^T) -(correct answer)True Effect of swapping rows on
determinant -(correct answer)Changes sign Effect of a zero row/column or equal
rows/columns on determinant -(correct answer)0 Effect of multiplying row/column by k
-(correct answer)Multiplied by k Effect of adding rows or multiples of rows to eachother on
determinant -(correct answer)No change A matrix is invertible if its determinant is 0 -(correct
answer)False (noninvertible) det(AB) = det(A) * det(B) -(correct answer)True det(A^-1) = det(A)
-(correct answer)False (1/det(A)) Ax = 0 has only the trivial solution if det(A) = 0 -(correct
answer)False (has a nontrivial solution if this is true) adj(A): each entry is the corresponding
entry's _____. -(correct answer)Cofactor What is the name of the following process: Ax = b x1
= det(A1)/det(A) etc. where An is the matrix made by deleting the nth column of A with b
-(correct answer)Cramer's rule What is a set of vectors called if: The set spans V Vectors are
liniearly independent All vectors are distinct and nonzero -(correct answer)Basis for V What
does the following process find: RREF the matrix for (av1 +bv2 + cv3 = 0) Take the numbers of
