UMBC MATH 221: FINAL EXAM
QUESTIONS AND ANSWERS. VERIFIED
2026.
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] - 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])
What is a cofactor? - ANS C(ij) = (-1)^(i + j) * det A(ij)
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)
@COPYRIGHT 2026/2027 ALL RIGHTS RESERVED
1
QUESTIONS AND ANSWERS. VERIFIED
2026.
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] - 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])
What is a cofactor? - ANS C(ij) = (-1)^(i + j) * det A(ij)
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)
@COPYRIGHT 2026/2027 ALL RIGHTS RESERVED
1
