Question

(a) Write the following system as a matrix equation $A X=B$. SYSTEM $$\begin{array}{l} 5 x+3 y=4 \\ 3 x+2 y=3 \end{array}$$ Matrix equation $\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ $\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$ (b) The inverse of $A$ is $A^{-1}=$$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ (c) The solution of the matrix equation is $X=A^{-1} B$. $\left[\begin{array}{l}x \\ y\end{array}\right]$=$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ $\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$ (d) The solution of the system is $x=$_ $y=$ _.

Name: Problem 2, Chapter 6: College Algebra
Uploaded: 2020-08-06T07:28:41-08:00
Duration: 4 min 3 s
Channel: Ankit Gupta
Description: (a) Write the following system as a matrix equation A X=B. SYSTEM 5 x+3 y=4 3 x+2 y=3 Matrix equation [ □ □ □ □ ] [ □ □ ]=[ □ □ ] (b) The inverse of A is A^-1=[ □ □ □ □ ] (c) The solution of the matrix equation is X=A^-1 B. [ x y ]=[ □ □ □ □ ] [ □ □ ]=[ □ □ ] (d) The solution of the system is x= y= .

   (a) Write the following system as a matrix equation $A X=B$.
SYSTEM
$$\begin{array}{l}
5 x+3 y=4 \\
3 x+2 y=3
\end{array}$$
Matrix equation
$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$
$\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$
(b) The inverse of $A$ is $A^{-1}=$$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$
(c) The solution of the matrix equation is $X=A^{-1} B$.
$\left[\begin{array}{l}x \\ y\end{array}\right]$=$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$
$\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$
(d) The solution of the system is $x=$_____ $y=$ _____.

College Algebra

James Stewart,… 7th Edition

Chapter 6, Problem 2

Instant Answer

Solved by Expert Ankit Gupta

08/06/2020

Step 1

The matrix $A$ is formed by the coefficients of $x$ and $y$ in the system of equations, the matrix $X$ is formed by the variables $x$ and $y$, and the matrix $B$ is formed by the constants on the right side of the equations. So we Show more…

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(a) Write the following system as a matrix equation $A X=B$. SYSTEM $$\begin{array}{l} 5 x+3 y=4 \\ 3 x+2 y=3 \end{array}$$ Matrix equation $\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ $\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$ (b) The inverse of $A$ is $A^{-1}=$$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ (c) The solution of the matrix equation is $X=A^{-1} B$. $\left[\begin{array}{l}x \\ y\end{array}\right]$=$\left[\begin{array}{ll}\square & \square \\ \square & \square \end{array}\right]$ $\left[\begin{array}{l}\square \\ \square\end{array}\right]$=$\left[\begin{array}{l}\square \\ \square\end{array}\right]$ (d) The solution of the system is $x=$_____ $y=$ _____.

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Key Concepts

Fraction Simplification

Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor (GCD) to rewrite the fraction in its simplest form, which makes it easier to compare or perform arithmetic with other fractions.

Cross Multiplication

Cross multiplication is a method used to determine if two fractions are equivalent by multiplying the numerator of each fraction by the denominator of the other; if the products are equal, the fractions are equivalent.

Equivalent Fractions

This concept refers to fractions that may look different but represent the same value or portion of a whole when simplified or compared. Two fractions are equivalent if they yield the same quotient when their numerators are divided by their denominators.

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