Write a vector equation that is equivalent to the given syst

Write a vector equation that is equivalent to the given system of equations. x_2 + 2x_3 = 0 4x-, +8x_2- x_3 = 0 - x_1 + 4x_2 - 6x_3 = 0

Solution

The given system of linear equations is

0x₁ + x₂ + 2x₃ = 0

4x₁ + 8x₂ -x₃ = 0 and

(-1)x₁ + 4x₂ - 6x₃ = 0

The 3x3 coefficient matrix will have the rows ( 0, 1, 2), (4, 8, -1) and ( -1, 4, -6) .Thus, the columns of the coeffient matrix will be ( 0, 4, -1)^T , (1, 8, 4)^T and ( 2, -1, -6)^T . The given system of linear equations can be written as x₁ ( 0, 4, -1)^T + x₂ (1, 8, 4)^T + x₃ ( 2, -1, -6)^T = ( 0, 0,0)^T Thus the answer C is correct.