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Zorluk: KolayMatrices and Determinants

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

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

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

Determinant of a 2x2 Matrix
Tahmini Süre:45s
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Konular

Matrices and Determinants

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