Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Use Cramer’s rule to compute the solutions of the systems in Exercises 1–6.$$\begin{aligned} x_{1}+3 x_{2}+x_{3} &=4 \\-x_{1}+& 2 x_{3}=2 \\ 3 x_{1}+x_{2} &=2 \end{aligned}$$

$x_{1}=0.4$$x_{2}=0.8$$x_{3}=1.2$

Algebra

Chapter 3

Determinants

Section 3

Cramer’s Rule, Volume, and Linear Transformations

Introduction to Matrices

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

07:29

Use Cramer’s rule to compu…

02:47

03:07

03:02

02:26

07:14

In Exercises 29–36, use Cr…

05:46

06:14

09:30

06:49

in this video, I'm gonna be going over how to do problem number six. Uh, session They're going three, which is based on determines in the Cramer's rule. And I did everything beforehand because the determinants of three by three take are very time consuming and very long, So I'll just go through how I did this problem. Um, I didn't go over it once, but the video, then upward properly. So, uh, I'll just go over roughly. Um, it's pretty simple is just like solving a problem, too. And for except this time instead of two by two, it's a three by three. So that's more mathematically, a little bit difficult. So to start off were given this set of system of equations and that would make this problem this have a problem a lot easier if you were toe. Visualize it in a X equals B matrix form. Like this, uh, that I underline just now, um, so here the problem is asking us to solve, uh, system using the Cramer's rule, which is basically says that if we were a substitute 4 to 2, which is, uh, here is be label be into each column of a and take it. The determinant. The rest of the matrix is a, um, and divided by the initial initial determinant when, without substituting be into it. Um, then we would get every single solution to the system equations. So here to start off, I first took the initial determinant of A without swapping anything. I'm to take the determinant of the three right to be, um, you're basically for the for the first moment you do one times the determinant of this square two by two, right here and then minus three times the determinant of the outer two by two closer, one times the determinant of the 1st 2 columns. Right here. Well, sorry if it's a little bit messy, cause I keep going over what I've drawn over previously. So here we got, um, negative to minus negative 18 minus one, which is which ends up being a negative too close. 18 minus one, which is 15 for the initial determinant. And then we, um and then for the first time of the creamers are always swap the first row with 4 to 2 and take it to determine which comes out to be six, and we repeat the same for the other two rows where when we swapped the second row with 4 to 2, Um, which is which is Ah Bee column. We got the determinant to be 12. And when we do so with the third column, we get the determined to be 18 um, and take out the solution to the system of equations. We just divide these determinant values by the initial determinant to get each value of the X column vector. That would be this. That was service a solution to the system equations he wrecks. One is six, divided by 15 extra. Strolled the water by 15 Extras 18 Divided by 15 um, and which gives us these Nissen, while is, respectively.

View More Answers From This Book

Find Another Textbook

In mathematics, the absolute value or modulus |x| of a real number x is its …

Use Cramer’s rule to compute the solutions of the systems in Exercises 1–6.<…

In Exercises 29–36, use Cramer’s Rule to solve each system.$$\left\{\beg…

05:06

02:43

Given subspaces $H$ and $K$ of a vector space $V,$ the sum of $H$ and $K,$ w…

02:23

In Exercises 21 and $22,$ find a parametric equation of the line $M$ through…

01:30

$[\mathbf{M}]$ If det $A$ is close to zero, is the matrix $A$ nearly singula…

01:37

Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why…

03:27

In Exercises $3-6,$ find an explicit description of Nul $A$ by listing vecto…

03:25

In Exercises 15 and $16,$ find $A$ such that the given set is $\operatorname…

04:16

Suppose $A$ is a $3 \times 3$ matrix and $y$ is a vector in $\mathbb{R}^{3}$…

01:29

Let $A$ be an $m \times n$ matrix, and let $\mathbf{u}$ and $\mathbf{v}$ be …

04:41

In Exercises $29-32,$ (a) does the equation $A \mathbf{x}=0$ have a nontrivi…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.