Answer:
7519 is already in the simplest form. It can be written as 3.947368 in decimal form (rounded to 6 decimal places).
Step-by-step explanation:
Answer:
![\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%200%20%26%200%26%2046%2F41%20%26180%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Step-by-step explanation:
From the question we are told that
System of equations given as
x₁ + 3x₂ + x₃ + x₄ = 3;
2x₁ - 2x₂ + x₃ + 2x₄ = 8;
x₁ - 5x₂ + x₄ = 5
Matrix form
![\begin{Vmatrix}x_1\\x_2\\x_3\\x_4\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7Dx_1%5C%5Cx_2%5C%5Cx_3%5C%5Cx_4%5Cend%7BVmatrix%7D)
Generally the echelon reduction is mathematically applied as
![\begin{Vmatrix}1 & 3 & 1&1&3\\2 & -2 & 1&2&8\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C2%20%26%20-2%20%26%201%262%268%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Add -2 times the 1st row to the 2nd row
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & -8 & -1&0&2\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%20-8%20%26%20-1%260%262%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Multiply the 2nd row by -1/8
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&1 & -5 & 1& 5\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%261%20%26%20-5%20%26%201%26%205%5Cend%7BVmatrix%7D)
Add -1 times the 2nd row to the 3rd row
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & -41/8 & 1& 21/4\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%260%20%26%20-41%2F8%20%26%201%26%2021%2F4%5Cend%7BVmatrix%7D)
Multiply the 3rd row by -8/41
![\begin{Vmatrix}1 & 3 & 1&1&3\\0 & 1 & 1/8&0&-1/4\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%201%261%263%5C%5C0%20%26%201%20%26%201%2F8%260%26-1%2F4%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Add -1/8 times the 3rd row to the 2nd row
Add -1 times the 3rd row to the 1st row
![\begin{Vmatrix}1 & 3 & 0&49/41&165/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%203%20%26%200%2649%2F41%26165%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Add -3 times the 2nd row to the 1st row
![\begin{Vmatrix}1 & 0 & 0& 46/41 &180/41\\0 & 1 & 0&1/41 &-5/41\\0&0 & 1 & -8/41& -42/41\end{Vmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7BVmatrix%7D1%20%26%200%20%26%200%26%2046%2F41%20%26180%2F41%5C%5C0%20%26%201%20%26%200%261%2F41%20%26-5%2F41%5C%5C0%260%20%26%201%20%26%20-8%2F41%26%20-42%2F41%5Cend%7BVmatrix%7D)
Hmm question is a little confusing but fractions can be represented as division or a part of somthing, like 4 pieces of an 8 slice pizza, or you have 8 peices of pizza and you divide them by 4. Im pretty sure a rational number is any number that can be representated as a fraction. an irrational number is something you cant express as a fraction like the square root of a number or pi.