Write the given system of equations as a matrix equation and solve using inverses. Complete parts a through...

Question

Write the given system of equations as a matrix equation and solve using inverses. Complete parts a through c.
x1 - 3x2 = k1
x2 + x3 = k2
4x1 - x2 + 10x3 = k3
a. What are x1, x2, and x3 when k1 = 1, k2 = 0, and k3 = 4?

SnapAndSolve AI · Accepted Answer

To solve the system of equations using matrix inverses, we first write the system in matrix form:

Matrix Equation:

[ [1, -3, 0], [0, 1, 1], [4, -1, 10] ] * [x1, x2, x3] = [k1, k2, k3]

Substitute k1 = 1, k2 = 0, and k3 = 4:

[ [1, -3, 0], [0, 1, 1], [4, -1, 10] ] * [x1, x2, x3] = [1, 0, 4]

Find the inverse of the coefficient matrix and multiply it by the constants matrix:

Calculate the inverse of the coefficient matrix:

Inverse = [ [10/31, 3/31, 1/31], [4/31, 1/31, -1/31], [-1/31, -1/31, 1/31] ]

Multiply the inverse by the constants matrix:

[x1, x2, x3] = [ [10/31, 3/31, 1/31], [4/31, 1/31, -1/31], [-1/31, -1/31, 1/31] ] * [1, 0, 4]

Result:

x1 = 13/31, x2 = 3/31, x3 = 1/31

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Write the given system of equations as a matrix equation and solve using inverses. Complete parts a through...

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