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asked 2021-06-10

Determine whether the given set S is a subspace of the vector space V.

A. V=\(P_5\), and S is the subset of \(P_5\) consisting of those polynomials satisfying p(1)>p(0).

B. \(V=R_3\), and S is the set of vectors \((x_1,x_2,x_3)\) in V satisfying \(x_1-6x_2+x_3=5\).

C. \(V=R^n\), and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.

D. V=\(C^2(I)\), and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.

E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.

F. V=\(P_n\), and S is the subset of \(P_n\) consisting of those polynomials satisfying p(0)=0.

G. \(V=M_n(R)\), and S is the subset of all symmetric matrices

A. V=\(P_5\), and S is the subset of \(P_5\) consisting of those polynomials satisfying p(1)>p(0).

B. \(V=R_3\), and S is the set of vectors \((x_1,x_2,x_3)\) in V satisfying \(x_1-6x_2+x_3=5\).

C. \(V=R^n\), and S is the set of solutions to the homogeneous linear system Ax=0 where A is a fixed m×n matrix.

D. V=\(C^2(I)\), and S is the subset of V consisting of those functions satisfying the differential equation y″−4y′+3y=0.

E. V is the vector space of all real-valued functions defined on the interval [a,b], and S is the subset of V consisting of those functions satisfying f(a)=5.

F. V=\(P_n\), and S is the subset of \(P_n\) consisting of those polynomials satisfying p(0)=0.

G. \(V=M_n(R)\), and S is the subset of all symmetric matrices

asked 2021-06-25

The row echelon form of a system of linear equations is given.

(a)Writethesystemofequationscorrespondingtothegivenmatrix.Usex,y;orx,y,z;or x_1,x_2,x_3,x_4 asvariables.

(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. \left[ 10215−1 \right]

(a)Writethesystemofequationscorrespondingtothegivenmatrix.Usex,y;orx,y,z;or x_1,x_2,x_3,x_4 asvariables.

(b)Determinewhetherthesystemisconsistentorinconsistent.Ifitisconsistent,givethesolution. \left[ 10215−1 \right]

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 2020-12-25

Use cramer's rule to solve system of linear equations

\(13x-6y=17\)

\(26x-12y=8\)

asked 2021-02-21

\(\begin{cases}1x_1-2x_2=-16\\1x_1-1x_2=-11\end{cases}\)

asked 2021-03-10

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

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

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

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

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

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

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

asked 2021-04-06

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

13x-6y=17

26x-12y=8

13x-6y=17

26x-12y=8

asked 2021-02-04

\(\begin{cases}20x+8y=11\\12x-24y=21\end{cases}\)

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 2021-01-13

Use cramer's rule to solve

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

\(0.2x_1+0.3x_2=0.6\)

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

\(0.2x_1+0.3x_2=0.6\)