Question

asked 2021-02-18

Use an inverse matrix to solve system of linear equations.

\(x+2y=-1\)

\(x-2y=3\)

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 2021-03-12

(5,3)

\(x-y=2\)

\(x+y=8\)

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.

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 2021-03-10

\(2x+4y=10\)

\(\displaystyle-{\frac{{{1}}}{{{2}}}}{x}+{3}={y}\)

Find the solution to the system of equations.

A. (0, -3)

B. (-6, 0)

C. There are infinite solutions.

D. There are no solutions.

asked 2021-03-15

Use back-substitution to solve the system of linear equations.

\(\displaystyle{b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{x}&-{y}&+{5}{z}&={26}\backslash&\ \ \ {y}&+{2}{z}&={1}\backslash&&\ \ \ \ \ {z}&={6}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}\)

(x,y,z)=()

\(\displaystyle{b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{x}&-{y}&+{5}{z}&={26}\backslash&\ \ \ {y}&+{2}{z}&={1}\backslash&&\ \ \ \ \ {z}&={6}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}\)

(x,y,z)=()

asked 2020-10-23

Determine if (1,3) is a solution to the given system of linear equations.

\(5x+y=8\)

\(x+2y=5\)

asked 2021-03-05

\(3x+7y-20z=-4\)

\(5x+12y-34z=-7\)

asked 2021-03-10

Use Cramer's rule to solve the given system of linear equations.

\(\displaystyle{x}_{{{1}}}-{x}_{{{2}}}+{4}{x}_{{{3}}}=-{2}\)

\(\displaystyle-{8}{x}_{{{1}}}+{3}{x}_{{{2}}}+{x}_{{{3}}}={0}\)

\(\displaystyle{2}{x}_{{{1}}}-{x}_{{{2}}}+{x}_{{{3}}}={6}\)

\(\displaystyle{x}_{{{1}}}-{x}_{{{2}}}+{4}{x}_{{{3}}}=-{2}\)

\(\displaystyle-{8}{x}_{{{1}}}+{3}{x}_{{{2}}}+{x}_{{{3}}}={0}\)

\(\displaystyle{2}{x}_{{{1}}}-{x}_{{{2}}}+{x}_{{{3}}}={6}\)