Question

Write the system as a vector equation or matrix equation as indicated. Write the following system as a matrix equation involving the product of a matrix and a vector on the left side and a vector on the right side. 2x1 x2 - 5x3

Answer 1

Explanation:

The complete system of equations are:

`2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 =3`

From above; the equation can be re-written as:

`2x_1 +x_2 -5x_3 = 4 \\ \\ 5x_1 -5x_2 +0x_3=3`;

However; writing the system as a matrix equation in form:

`A \ x ^(\to )= b ^(\to)`

where;

A = coefficient matrix ;
`x^(\to)` = variable vector ; and,
`b ^(\to)` = constant vector

Then:

The coefficients of
`x_ 1 \ and\ x_1 = \left[\begin{array}{c}2\\5\\\end{array}\right]`

The coefficients of
`x_ 2 \ and\ x_2 = \left[\begin{array}{c}1\\-5\\\end{array}\right]`

The coefficients of
`x_ 3 \ and\ x_3 = \left[\begin{array}{c}-5\\0\\\end{array}\right]`

∴

`\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right] \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] = \left[\begin{array}{c}4\\3\\\end{array}\right]`

Finally;

the coefficient of matrix A =
`\left[\begin{array}{ccc}2&1&-5\\5&-5&0\\\end{array}\right]`

`x^(\to) = \left[\begin{array}{c}x_1\\x_2\\\end{array}\right] \implies variable \ vector`

`b^(\to) = \left[\begin{array}{c}4\\3\\\end{array}\right]\implies constant \ vector`