Let's solve the given system of equations step-by-step to find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex]:
We are given the equations in matrix form:
[tex]\[
\left[\begin{array}{c}
2ab - 1 \\
4 - b
\end{array}\right]
=
\left[\begin{array}{c}
1 \\
3
\end{array}\right]
\][/tex]
This can be written as two separate equations:
1. [tex]\(2ab - 1 = 1\)[/tex]
2. [tex]\(4 - b = 3\)[/tex]
### Step 1: Solve the second equation for [tex]\(b\)[/tex]
The second equation is:
[tex]\[
4 - b = 3
\][/tex]
To solve for [tex]\(b\)[/tex], isolate [tex]\(b\)[/tex]:
[tex]\[
4 - b = 3 \\
4 - 3 = b \\
b = 1
\][/tex]
Now that we have found [tex]\(b = 1\)[/tex], we can substitute this value into the first equation.
### Step 2: Substitute [tex]\(b = 1\)[/tex] into the first equation and solve for [tex]\(a\)[/tex]
The first equation is:
[tex]\[
2ab - 1 = 1
\][/tex]
Substitute [tex]\(b = 1\)[/tex]:
[tex]\[
2a(1) - 1 = 1 \\
2a - 1 = 1
\][/tex]
Next, isolate [tex]\(a\)[/tex]:
[tex]\[
2a - 1 = 1 \\
2a = 1 + 1 \\
2a = 2 \\
a = \frac{2}{2} \\
a = 1
\][/tex]
### Final Result
Therefore, the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] that satisfy the system of equations are:
[tex]\[
a = 1, \quad b = 1
\][/tex]
