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UMBC MATH 221: Final Exam Questions | Accurate &
Verified Answers to Pass Actual Exam
How do you calculate the determinant of a 2x2 matrix?
A = [a b , c d]
Ans: det A = ad - bc
How do you calculate the determinant of a 3x3 matrix?
A = [a11 a12 a13 , a21 a22 a23 , a31 a32 a33]
Assignment Expert
Ans: det A = (a11 * det [a22 a 32 , a23 a33]) + (-1)(a12 * det [a21 a 31 , a23
a33]) + (-1)(-1)(a13 * det [a21 a31 , a22 a32])
Guru01 - Stuvia
What is a cofactor?
Ans: C(ij) = (-1)^(i + j) * det A(ij)
2026
What does Theorem 1 (ch 3) state? (Cofactor expansions)
Ans: The determinant of any matrix can be computed by a cofactor
©
expansion across any row or down any column:
det A = (ai1 * Ci1) + ... + (ain * Cin)
OR
det A = (a1j * C1j) + ... + (anj * Cnj)
What does Theorem 2 (ch 3) state? (A is triangular)
Ans: If A is a triangular matrix, then det A is the product of the entries of
the main diagonal of A
What does Theorem 3 (ch 3) state? (Row operations)
Ans: If A is a square matrix:
UMBC MATH 221: Final Exam Questions | Accurate &
Verified Answers to Pass Actual Exam
How do you calculate the determinant of a 2x2 matrix?
A = [a b , c d]
Ans: det A = ad - bc
How do you calculate the determinant of a 3x3 matrix?
A = [a11 a12 a13 , a21 a22 a23 , a31 a32 a33]
Assignment Expert
Ans: det A = (a11 * det [a22 a 32 , a23 a33]) + (-1)(a12 * det [a21 a 31 , a23
a33]) + (-1)(-1)(a13 * det [a21 a31 , a22 a32])
Guru01 - Stuvia
What is a cofactor?
Ans: C(ij) = (-1)^(i + j) * det A(ij)
2026
What does Theorem 1 (ch 3) state? (Cofactor expansions)
Ans: The determinant of any matrix can be computed by a cofactor
©
expansion across any row or down any column:
det A = (ai1 * Ci1) + ... + (ain * Cin)
OR
det A = (a1j * C1j) + ... + (anj * Cnj)
What does Theorem 2 (ch 3) state? (A is triangular)
Ans: If A is a triangular matrix, then det A is the product of the entries of
the main diagonal of A
What does Theorem 3 (ch 3) state? (Row operations)
Ans: If A is a square matrix:
