(a) Evaluate the matrix product, Ax, where 𝐀=[ 7 5 1 3 ] and 𝐱=[ x

Name: Problem 16, Chapter 7: Mathematics for Economics and Business
Uploaded: 2022-01-31T19:37:11-08:00
Duration: 1 min 58 s
Channel: Niamat Khuda
Description: (a) Evaluate the matrix product, Ax, where 𝐀=[ 7 5 1 3 ] and 𝐱=[ x y ] Hence show that the system of linear equations 7 x+5 y=3 x+3 y=2 can be written as 𝐀 𝐱=𝐛 where 𝐛=[ 3 2 ]. (b) The system of equations 2 x+3 y-2 z=6 x-y+2 z=3 4 x+2 y+5 z=1 can be expressed in the form A x=b. Write down the matrices A, x and b.

step 1 Hey guys, that's to problem 16. In this problem, we need to evaluate the matrix product, a multi

Question

(a) Evaluate the matrix product, $\mathrm{Ax}$, where $$ \mathbf{A}=\left[\begin{array}{ll} 7 & 5 \\ 1 & 3 \end{array}\right] \text { and } \quad \mathbf{x}=\left[\begin{array}{l} x \\ y \end{array}\right] $$ Hence show that the system of linear equations $$ \begin{array}{r} 7 x+5 y=3 \\ x+3 y=2 \end{array} $$ can be written as $\mathbf{A x}=\mathbf{b}$ where $\mathbf{b}=\left[\begin{array}{l}3 \\ 2\end{array}\right]$. (b) The system of equations $$ \begin{array}{r} 2 x+3 y-2 z=6 \\ x-y+2 z=3 \\ 4 x+2 y+5 z=1 \end{array} $$ can be expressed in the form $A x=b$. Write down the matrices $A, x$ and $b$.

    (a) Evaluate the matrix product, $\mathrm{Ax}$, where
$$
\mathbf{A}=\left[\begin{array}{ll}
7 & 5 \\
1 & 3
\end{array}\right] \text { and } \quad \mathbf{x}=\left[\begin{array}{l}
x \\
y
\end{array}\right]
$$
Hence show that the system of linear equations
$$
\begin{array}{r}
7 x+5 y=3 \\
x+3 y=2
\end{array}
$$
can be written as $\mathbf{A x}=\mathbf{b}$ where $\mathbf{b}=\left[\begin{array}{l}3 \\ 2\end{array}\right]$.
(b) The system of equations
$$
\begin{array}{r}
2 x+3 y-2 z=6 \\
x-y+2 z=3 \\
4 x+2 y+5 z=1
\end{array}
$$
can be expressed in the form $A x=b$. Write down the matrices $A, x$ and $b$.

Mathematics for Economics and Business

lan Jacques 5th Edition

Chapter 7, Problem 16

Instant Answer

Solved by Expert Niamat Khuda

01/31/2022

Step 1

The matrix $\mathbf{A}$ is given as $$ \mathbf{A}=\left[\begin{array}{ll} 7 & 5 \\ 1 & 3 \end{array}\right] $$ and the vector $\mathbf{x}$ is given as $$ \mathbf{x}=\left[\begin{array}{l} x \\ y \end{array}\right] $$ The matrix product $\mathbf{Ax}$ is computed as Show more…

Show all steps

Thanks for your feedback!

(a) Evaluate the matrix product, $\mathrm{Ax}$, where $$ \mathbf{A}=\left[\begin{array}{ll} 7 & 5 \\ 1 & 3 \end{array}\right] \text { and } \quad \mathbf{x}=\left[\begin{array}{l} x \\ y \end{array}\right] $$ Hence show that the system of linear equations $$ \begin{array}{r} 7 x+5 y=3 \\ x+3 y=2 \end{array} $$ can be written as $\mathbf{A x}=\mathbf{b}$ where $\mathbf{b}=\left[\begin{array}{l}3 \\ 2\end{array}\right]$. (b) The system of equations $$ \begin{array}{r} 2 x+3 y-2 z=6 \\ x-y+2 z=3 \\ 4 x+2 y+5 z=1 \end{array} $$ can be expressed in the form $A x=b$. Write down the matrices $A, x$ and $b$.

Play audio

Feedback

Niamat Khuda and 54 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Matrix-Vector Multiplication

Matrix-vector multiplication is a fundamental operation in linear algebra where each entry in the resulting vector is computed as the dot product of a row from the matrix with the vector. This operation combines linear combinations of the vector's components, reflecting the structure of linear transformations and systems of equations.

Representation of Linear Systems in Matrix Form

Representing a system of linear equations as Ax=b involves arranging the coefficients of the variables into a matrix A, the unknowns into a vector x, and the constants into a vector b. This form simplifies the analysis and solution of the system using linear algebra techniques, making it easier to apply systematic methods such as Gaussian elimination, matrix inverses, and others.

Please give Ace some feedback