Calxsolver
Subject:  Linear Algebra

Inverse of [[2, 1, 1], [1, 3, 2], [1, 0, 0]]

Use Gauss-Jordan elimination on the augmented [A | I] matrix.

Answer [[0, 0, 1], [-2, 1, 3], [3, -1, -5]]

Solution

  1. Matrix [[2, 1, 1], [1, 3, 2], [1, 0, 0]]
  2. Determinant det = -1
  3. Method Augment with the identity, then Gauss-Jordan eliminate.
  4. Inverse [[0, 0, 1], [-2, 1, 3], [3, -1, -5]]

Try a similar problem yourself

Use the Matrix Inverse to solve a similar problem with your own values.

Open the solver

More Linear Algebra problems

Determinant of [[3, 1], [4, 2]] Apply the 2×2 determinant formula det = ad − bc. Determinant of the 3×3 matrix [[1, 2, 3], [4, 5, 6], [7, 8, 10]] Use cofactor expansion along the first row. Multiply [[1, 2], [3, 4]] · [[5, 6], [7, 8]] Combine rows of A with columns of B to compute the product. Inverse of [[4, 7], [2, 6]] Check that the determinant is non-zero, then apply the 2×2 inverse formula. Add [[1, 2], [3, 4]] + [[5, 6], [7, 8]] Add two matrices of the same shape entry by entry. Dot product (1, 2, 3) · (4, 5, 6) Multiply matching components and sum to find the dot product.