Examkin

Question

Difficulty: EasyMatrices and Determinants

What is the determinant of the matrix A=(6−321)A = \begin{pmatrix} 6 & -3 \\ 2 & 1 \end{pmatrix}?

  1. 12Answer
  2. B
    0
  3. C
    -12
  4. D
    -36

Answer

12
For any 2×22 \times 2 matrix (abcd)\begin{pmatrix} a & b \\ c & d \end{pmatrix}, the determinant is given by ad−bcad - bc. Substituting a=6a = 6, b=−3b = -3, c=2c = 2, and d=1d = 1 yields (6)(1)−(−3)(2)=6−(−6)=12(6)(1) - (-3)(2) = 6 - (-6) = 12.

Step-by-Step Solution

1
Identify the elements of the 2x2 matrix A=(abcd)A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
a=6a = 6, b=−3b = -3, c=2c = 2, d=1d = 1
Standard entries for determinant formula det⁡(A)=ad−bc\det(A) = ad - bc.
2
Compute the product of the main diagonal elements (adad) and off-diagonal elements (bcbc)
ad=(6)(1)=6ad = (6)(1) = 6 and bc=(−3)(2)=−6bc = (-3)(2) = -6
These form the components of the 2x2 determinant formula.
3
Subtract bcbc from adad
det⁡(A)=6−(−6)=6+6=12\det(A) = 6 - (-6) = 6 + 6 = 12
Subtracting a negative quantity is equivalent to addition.

Key Concept

Determinant of a 2x2 Matrix
Estimated Time:45s
Rate this question

Topics

Matrices and Determinants

More questions from this topic