Reference no: EM132463208

Linear Algebra Problems -

Problem 1 - Determine if the following system is consistent:

x₂ - 4x₃ = 8

2x₁ - 3x₂ + 2x₃ = 1

5x₁ - 8x₂ + 7x₃ = 1

Problem 2 - Given any constants a, b, c where a ≠ 0, find all values of x such that the matrix A is invertible

Problem 3 - Determine all eigenvalues and their algebraic multiplicities of the matrix

where a is a real number.

Problem 4 - Is (3, 4, -1) a solution of the following system?

5x₁ - x₂ + 2x₃ = 9

-2x₁ + 6x₂ + 9x₃ = 9

-7x₁ + 5x₂ - 3x₃ = 1

Problem 5 - For what values of h and k is the following system consistent?

2x₁ - x₂ = h

-4x₁ + 2x₂ = k.