The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the eigenvalue method to find a general solution of the system. ×₁ = 3×₁ + 3x2 + 2x3, x2' = -2x₁ - 2x2 - 3x3, x3' = 2x₁ + 2x2 + 3x3

Explain how to find the determinant of a 22 matrix.

Explain what it means in terms of an inverse for a matrix to have a 0 determinant.

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

Can a matrix that has 0 entries for an entire row have one solution? Explain why or why not.

One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a system of linear equations to determine how many liters of each solution are required to obtain the desired mixture. Solve the system using matrices.