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I agree. To me it makes more sense to continure with row reduction, not stop in the middle.Simon Bridge said:The second box gives the rather weird construction
Simon Bridge said:The matrix has a column of zeros ... look through your notes to find out what that means.
The 1st box gives equations:
##0x_1 + x_2 + 4x_3 = 0##
##0x_1 -x_2 + 6x_3 = 0##
The second box gives the rather weird construction:
$$\frac{x_1}{6+4}=\frac{x_2}{0-0} = \frac{x_3}{0-0}$$
... it looks like it is trying to show you something about a technique already used before.
I wouldn't do it that way. I'd just solve the simultaneous equations.
ok thanks for your idea palMark44 said:I agree. To me it makes more sense to continure with row reduction, not stop in the middle.
##\begin{bmatrix} 0 & 1 & 4 \\ 0 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix} \equiv \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0\end{bmatrix}##
I've skipped a couple of steps here.
That last matrix represents this system:
##x_2 = 0##
##x_3 = 0##
##x_1## doesn't appear, which means it is arbitrary, all possible eigenvectors are ##k \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}##
I agree. I also don't believe @saranga's intent was to be sarcastic.Stephen Tashi said:From my (USA) point of view "thanks pal" isn't offensive or sarcastic. However, it is anachronistic - it sounds like common speech from from 1940's. Someone can probably cite a film where Humphrey Bogart says it.
"With all due respect" is fine. Based on the IP address, the OP is posting from Asia, so I really don't believe there was any sarcastic intent. Can we drop this now?Simon Bridge said:It's not "pal" by itself that denotes sarcasm - it's the construct and context that makes it ambiguous, but I may be being too sensitive here - so nobody has ever heard "thanks pal" sarcastically? Maybe that has fallen out of use too?
Don't get me wrong, it can be OK here too ... you need the intonation to tell the difference and the anachronism in writing it down can primes the reader to question the intent. My point is not that I thought the intent was sarcastic but that I could not tell... especially as the question we all answered was not strictly the one asked.
If you don't understand the way the book does it then do it another way that you do understand... oh gee, thanks pal, I didn't think of that already...
These things can change, maybe I'm out of date? - is "with all due respect" still OK in the US?
To solve simultaneous equations using matrices, first write the equations in matrix form with the coefficients of the variables on the left side and the constants on the right side. Then, use Gaussian elimination or other matrix operations to reduce the matrix to its row-echelon form. Finally, use back-substitution to find the values of the variables.
Using matrices to solve simultaneous equations can save time and make the calculations more organized. It also allows for solving larger systems of equations with more variables.
Yes, matrices can be used to solve any system of linear equations. However, if the system is inconsistent or has no unique solution, the matrix operations will not be possible.
The inverse matrix method involves finding the inverse of the coefficient matrix and multiplying it by the constant matrix to obtain the solution. This method is useful for solving systems of equations with a small number of variables.
Matrices can only be used to solve systems of linear equations. Non-linear equations cannot be solved using matrices. Additionally, if the coefficient matrix is singular, the inverse matrix method cannot be used and other methods must be applied.