Question

Consider the following system of linear equations.

a) x1 +x2 +x3 +x4 =10

b) 2x1 +3x2 +5x3 +x4 =−7

c) x1 − x2 + 8x3 = 6
Define A to be the matrix of coefficients. Write the above system into the form Ax = b where x is the vector of unknown and b the vector of solution.

Answer 1

To write the system of linear equations into the form Ax = b, we arrange the coefficients of the variables into matrix A, the unknown variables into vector x, and the constants into vector b.

Step-by-step explanation:

To write the given system of linear equations in the form of Ax = b, we need to arrange the equations such that the coefficients of x variables are in matrix A, the unknown variables x form the vector x, and the constants on the right side form the vector b.

Given system of equations:

a) x1 + x2 + x3 + x4 = 10

b) 2x1 + 3x2 + 5x3 + x4 = -7

c) x1 - x2 + 8x3 = 6

Writing in the form Ax = b:

• Coefficients matrix A: [[1, 1, 1, 1], [2, 3, 5, 1], [1, -1, 8, 0]]
• Unknown variables vector x: [x1, x2, x3, x4]
• Constants vector b: [10, -7, 6]