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

21Singular matrix, det=0

For which k\displaystyle k is A=[1k26]\displaystyle A = \begin{bmatrix}1 & k\\2 & 6\end{bmatrix} singular?

A matrix is singular when its determinant is 0. Here det(A) = 1·6 − k·2 = 6 − 2k, so setting 6 − 2k = 0 gives k = 3. Check: 6 − 2(3) = 0.

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