Question

asked 2021-02-21

Cramer’s Rule to solve (if possible) the system of linear equations.

\(\displaystyle{\frac{{{5}}}{{{6}}}}{x}_{{1}}-{x}_{{2}}=-{20}\)

\(\displaystyle{\frac{{{3}}}{{{4}}}}{x}_{{1}}-{\frac{{{7}}}{{{2}}}}{x}_{{2}}=-{51}\)

\(\displaystyle{\frac{{{5}}}{{{6}}}}{x}_{{1}}-{x}_{{2}}=-{20}\)

\(\displaystyle{\frac{{{3}}}{{{4}}}}{x}_{{1}}-{\frac{{{7}}}{{{2}}}}{x}_{{2}}=-{51}\)

asked 2021-01-13

Use cramer's rule to solve

\(-0.4x_1+0.8x_2=1.6\)

\(0.2x_1+0.3x_2=0.6\)

\(-0.4x_1+0.8x_2=1.6\)

\(0.2x_1+0.3x_2=0.6\)

asked 2020-11-30

Use Cramer’s Rule to solve (if possible) the system of linear equations.

2x-y=-10

3x+2y=-1

2x-y=-10

3x+2y=-1

asked 2020-11-06

A small grocer finds that the monthly sales y (in $) can be approximated as a function of the amount spent advertising on the radio \(x_1\)

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

(in $) and the amount spent advertising in the newspaper \(x_2\) (in $) according to \(y=ax_1+bx_2+c\)

The table gives the amounts spent in advertising and the corresponding monthly sales for 3 months.

\(\begin{array}{|c|c|c|}\hline \text { Advertising, } x_{1} & \text { Advertising, } x_{2} &\text{sales, y} \\ \hline $ 2400 & {$ 800} & {$ 36,000} \\ \hline $ 2000 & {$ 500} & {$ 30,000} \\ \hline $ 3000 & {$ 1000} & {$ 44,000} \\ \hline\end{array}\)

a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the monthly sales if the grocer spends $250 advertising on the radio and $500 advertising in the newspaper for a given month.

asked 2020-12-25

Use cramer's rule to solve system of linear equations

13x-6y=17

26x-12y=8

13x-6y=17

26x-12y=8

asked 2020-10-19

The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer \(x_1\) (in $1000) and on the square footage of the home \(x_2 (\text{ in } 100ft^2)\) according to \(y=ax_1+bx_2+c\)

The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the purchase price for a buyer who makes $100000 per year and wants a \(2500ft^2\) home.

The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. a) Use the data to write a system of linear equations to solve for a, b, and c.

b) Use a graphing utility to find the reduced row-echelon form of the augmented matrix.

c) Write the model \(y=ax_1+bx_2+c\)

d) Predict the purchase price for a buyer who makes $100000 per year and wants a \(2500ft^2\) home.

asked 2021-03-06

Cramer’s Rule to solve (if possible) the system of linear equations.

\(\displaystyle-{8}{x}_{{1}}+{7}{x}_{{2}}{\mid}-{10}{x}_{{3}}=-{151}\)

\(\displaystyle{12}{x}_{{1}}+{3}{x}_{{2}}-{5}{x}_{{3}}={86}\)

\(\displaystyle{15}{x}_{{1}}-{9}{x}_{{2}}+{2}{x}_{{3}}={187}\)

\(\displaystyle-{8}{x}_{{1}}+{7}{x}_{{2}}{\mid}-{10}{x}_{{3}}=-{151}\)

\(\displaystyle{12}{x}_{{1}}+{3}{x}_{{2}}-{5}{x}_{{3}}={86}\)

\(\displaystyle{15}{x}_{{1}}-{9}{x}_{{2}}+{2}{x}_{{3}}={187}\)

asked 2020-12-28

Write the vector form of the general solution of the given system of linear equations.

\(x_1+2x_2-x_3=0\)

\(x_1+x_2+x_3=0\)

\(x_1+3x_2-3x_3=0\)

\(x_1+2x_2-x_3=0\)

\(x_1+x_2+x_3=0\)

\(x_1+3x_2-3x_3=0\)

asked 2020-12-17

Write the vector form of the general solution of the given system of linear equations.

\(3x_1+x_2-x_3+x_4=0\)

\(2x_1+2x_2+4x_3-6x_4=0\)

\(2x_1+x_2+3x_3-x_4=0\)

\(3x_1+x_2-x_3+x_4=0\)

\(2x_1+2x_2+4x_3-6x_4=0\)

\(2x_1+x_2+3x_3-x_4=0\)

asked 2021-02-19

For the given a system of linear equations

4x+y-5z=8

-2x+3y+z=12

3x-y+4z=5

Use matrix inversion to solve simultaneous equations.

4x+y-5z=8

-2x+3y+z=12

3x-y+4z=5

Use matrix inversion to solve simultaneous equations.