silemus.
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  1. 23×33\times 3 determinant expansion
  2. 10Eigenvalues of a 3×33\times 3 matrix
  3. 12Eigenvector for eigenvalue 3
  4. 14Inverse of a 2×22\times 2 matrix
  5. 17Solving a 3×33\times 3 linear system
  6. 20System with no solution
  7. 21Singular matrix, det=0
  8. 22Eigenvalue zero of a matrix
  9. 27Null space of a matrix
  10. 37Volume via scalar triple product
  11. 43Characteristic polynomial, 2×22\times 2
  12. 47Orthogonal matrix check
  13. 48Gram-Schmidt second vector
  14. 49Least-squares line fit
  15. 50Coordinates in a new basis
  16. 51Distance point to plane

14Inverse of a 2×22\times 2 matrix

Let A=[4726]\displaystyle A = \begin{bmatrix}4 & 7\\2 & 6\end{bmatrix}. Find A−1\displaystyle A^{-1}; what is its entry in row 2, column 1?

For a 2×2 matrix, swap the diagonal entries, negate the off-diagonal ones, and divide by the determinant ad−bc = 24−14 = 10. That gives A⁻¹ = (1/10)[[6,−7],[−2,4]], so the entry in row 2, column 1 is −2/10 = −1/5.

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