My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Thanks Tree3Thanks
  • 1 Post By greg1313
  • 2 Post By jks
Reply
 
LinkBack Thread Tools Display Modes
August 20th, 2018, 05:33 PM   #1
Newbie
 
Joined: Aug 2018
From: HK

Posts: 17
Thanks: 0

Determinants and Inverses of Square Matrices

Solve |x^2 3X|* |1 x|= |2 0|
|1 2 | |3 -x| |0 1|


-8x^3 +12x^2 =2

8x^3 - 12x^2 = -2

4x^3 - 6x^2 = -1

2x (2x^2 - 3x) = -1

x = -1/2 OR -1 OR 2



This is how I calculated this question, but the model answers are 1/2 OR
1+(√3)/2 OR 1-(√3)/2.
hy2000 is offline  
 
August 20th, 2018, 05:36 PM   #2
Newbie
 
Joined: Aug 2018
From: HK

Posts: 17
Thanks: 0

The question should be a square matrice but I don't know how to type it in to the computer
hy2000 is offline  
August 20th, 2018, 06:08 PM   #3
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,878
Thanks: 1087

Math Focus: Elementary mathematics and beyond
Is this what you intended?

$$\begin{bmatrix}x^2&3x \\
1 & 2\end{bmatrix}
\cdot
\begin{bmatrix}1 & x \\
3 & -x\end{bmatrix}
=
\begin{bmatrix} 2 & 0 \\
0 & 1\end{bmatrix}$$

To observe the code, right click on the math and select "Show Math As" > "TeX Commands" from the context menu or quote this post and examine the contents of the reply window.
greg1313 is offline  
August 20th, 2018, 06:11 PM   #4
Newbie
 
Joined: Aug 2018
From: HK

Posts: 17
Thanks: 0

Yes, are there any steps wrong so I cannot calculate the correct answer?
hy2000 is offline  
August 20th, 2018, 06:34 PM   #5
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,878
Thanks: 1087

Math Focus: Elementary mathematics and beyond
Well, I get

$$\begin{bmatrix}x^2&3x \\
1 & 2\end{bmatrix}
\cdot
\begin{bmatrix}1 & x \\
3 & -x\end{bmatrix}
=
\begin{bmatrix}x^2+9x & x^3-3x^2 \\
7 & -x\end{bmatrix}
=
\begin{bmatrix} 2 & 0 \\
0 & 1\end{bmatrix}$$

so either I am mistaken or there is a problem somewhere...
Thanks from hy2000
greg1313 is offline  
August 20th, 2018, 08:07 PM   #6
jks
Senior Member
 
jks's Avatar
 
Joined: Jul 2012
From: DFW Area

Posts: 626
Thanks: 90

Math Focus: Electrical Engineering Applications
Here is what I get:

$\displaystyle
\left |
\begin{array} {c c}
x^2 & 3x \\
1 & 2
\end{array}
\right |
\cdot
\left |
\begin{array} {c c}
1 & x \\
3 & -x
\end{array}
\right |
=
\left |
\begin{array} {c c}
2 & 0 \\
0 & 1
\end{array}
\right |
$

Per WP:

$\displaystyle \left |
\begin{array} {c c}
a & b \\
c & d
\end{array}
\right |
=ad-bc$

So we get:

$\displaystyle
\begin{align}(2x^2-3x)(-x-3x)&=2-0 \\
(2x^2-3x)(-4x)&=2 \\
(2x^2-3x)(2x)&=-1
\end{align}$

Which I believe that you correctly derived.

W|A gives the solutions as:

$\displaystyle \frac{1}{2}, \quad \frac{1}{2} - \frac{\sqrt{3}}{2}, \quad \frac{1}{2} + \frac{\sqrt{3}}{2}$

so I think that the opening parenthesis were misplaced.
Thanks from greg1313 and hy2000
jks is offline  
August 21st, 2018, 02:50 AM   #7
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,878
Thanks: 1087

Math Focus: Elementary mathematics and beyond
Ahh... determinants! My mistake.

It's best to state the entire question in the post body to avoid such confusion (but then I could have been more careful).
greg1313 is offline  
August 21st, 2018, 05:48 AM   #8
Math Team
 
topsquark's Avatar
 
Joined: May 2013
From: The Astral plane

Posts: 1,888
Thanks: 767

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by hy2000 View Post
Solve |x^2 3X|* |1 x|= |2 0|
|1 2 | |3 -x| |0 1|
A quick comment: Mathematics is "case sensitive." That means that X and x are not the same variable.

-Dan
topsquark is online now  
August 21st, 2018, 05:43 PM   #9
Newbie
 
Joined: Aug 2018
From: HK

Posts: 17
Thanks: 0

Thanks a lot, I have tried both ways; by determinants and just multiplying the matrices together, they have the same result
hy2000 is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
determinants, inverses, matrices, square



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
An example of two square matrices A and B of sameorder for which AB=0 and BA not ZERO starbug7 Linear Algebra 3 May 19th, 2015 07:05 AM
inverses norm abrams Algebra 10 January 13th, 2012 02:49 AM
Sum of certain inverses mod p Pell's fish Number Theory 1 November 13th, 2011 05:51 PM
Matrices and Determinants prashantakerkar Linear Algebra 4 August 20th, 2011 10:18 AM
Non-square Matrices matrixman42 Linear Algebra 2 November 4th, 2007 08:18 PM





Copyright © 2018 My Math Forum. All rights reserved.