Linear Algebra - Solve $xa+yb=c$ For $x, Y \in \mathbb{C}$ And $a,b ...

1. 1. Home
   2. Questions
   3. Tags
   4. Users
   5. Unanswered
2. Teams

   Ask questions, find answers and collaborate at work with Stack Overflow for Teams.

   Try Teams for free Explore Teams
3. Teams

4. Ask questions, find answers and collaborate at work with Stack Overflow for Teams. Explore Teams

Teams

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

Learn more about Teams Solve $xa+yb=c$ for $x, y \in \mathbb{C}$ and $a,b,c\in\mathbb{C}^2$ Ask Question Asked 12 years, 10 months ago Modified 11 years, 6 months ago Viewed 2k times 2 $\begingroup$

Let $a=\pmatrix{1\\1}, b=\pmatrix{1\\2}, c=\pmatrix{2\\1}$. Solve $xa + yb = c$ for $x, y \in \mathbb{C}$.

Does this mean I do $$1x+1y=2$$ $$1x+2y=1$$ and would be the final answer?

• linear-algebra

Share Cite Follow edited Mar 2, 2013 at 1:50 Diego Silvera 1,7371818 silver badges3030 bronze badges asked Jan 30, 2012 at 0:07 KjXKjX 2722 bronze badges $\endgroup$ 7

• 2 $\begingroup$ For some reason you have switched from $1x+1y=2$ to $1x+2y=1$. Why? $\endgroup$ – Henry Commented Jan 30, 2012 at 0:12
• $\begingroup$ It's just basic algebra. If $xa+yb=c$, then $yb=c-xa$, then $y=\dfrac{c-xa}{b}$. So you have a straight line assuming b isn't zero. $\endgroup$ – simplicity Commented Jan 30, 2012 at 0:21
• $\begingroup$ I have changed the tag of Linear Algebra to Algebra-Precalculus. I don't see how this applies to Linear Algebra given the little information. $\endgroup$ – 000 Commented Jan 30, 2012 at 0:45
• $\begingroup$ Its a matrix. That is why. $\endgroup$ – KjX Commented Jan 30, 2012 at 1:24
• $\begingroup$ It is linear algebra but I dont know how to put it in matrix form form in the post I put $\endgroup$ – KjX Commented Jan 30, 2012 at 1:25

| Show 2 more comments

2 Answers 2

Sorted by: Reset to default Highest score (default) Date modified (newest first) Date created (oldest first) 1 $\begingroup$

Assuming Zev's edit is correct, then your equations $$1x+1y=2$$ $$1x+2y=1$$ are correct. To complete the problem, you need to find the values of $x$ and $y$ that make both of those equations true at the same time.

Hint: Subtract the first equation from the second equation.

Share Cite Follow answered Feb 11, 2012 at 6:26 IsaacIsaac 36.8k1515 gold badges110110 silver badges142142 bronze badges $\endgroup$ 1

• $\begingroup$ Someone is reading meta these days :) $\endgroup$ – P.K. Commented Dec 28, 2012 at 15:35

Add a comment | 0 $\begingroup$

$$1x+1y=2\cdots\cdots(1)$$ $$1x+2y=1\cdots\cdots(2)$$

Multiply (1) by -1 $$-1x-1y=-2 $$ Adding above and (2),

$$1x+2y -1x-1y=1-2$$ $$y=-1$$ Put it in (1) $$1x+1y=2$$ $$1x-1=2$$ $$x=3$$ Solution Set = (3,-1)

Verify this by putting in the 2 equations.

Share Cite Follow answered Feb 11, 2012 at 6:43 InquestInquest 6,68333 gold badges3838 silver badges5959 bronze badges $\endgroup$ Add a comment |

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged

• linear-algebra

.

• Featured on Meta
• More network sites to see advertising test [updated with phase 2]
• We’re (finally!) going to the cloud!

Related

1 Solve for eigenvector (complex eigenvalue) 0 Let $0 \ne u \in \mathbb{C}^n$ fixed and consider for every $v \in \mathbb{C}^n$ the matrix $E(v)=uv^*$. Find all eigenvalues of $E(v)$. 1 How to solve this matrix for h and k? 1 How do you set up an augmented matrix to solve for a Transformation matrix? 1 Don't understand what a problem in Artin's "Algebra" is asking for. 2 Given matrices $A$ and $B$, solve for $Z$ in the following equation: $A^{-4}BZ^{3}A^{5}B^{2}A=-3A^{-6}$ 0 Matrix transformation $f:\mathbb{R}^{3}\rightarrow \mathbb{R}^{3}$ 0 Solve for Vector q in q Equals Matrix P Times Vector q

Hot Network Questions

• Find the Smallest Data Type for a Number
• From exponent of sum to product of exponents
• How to find file names but only with grep .html OR .php?
• Is there a symbol for the Hyper key?
• What's a good way to append a nonce to ciphertext in Python for AES GCM in Python?
• Sequence with diagonal lines and circles
• Understanding the definition of the covariant derivative
• What was the significance of Mount Doom's eruption?
• Align TikZ pictures horizontally
• What style/Form is the Stranger's Poem in, from The Magnus Archives?
• Polynomial.java - a Java class for dealing with polynomials with BigDecimal coefficients
• What is the proper way to say "voice direction" in German?
• Why linear regression doing well in time series data?
• When my modem places a signal on coax, is that signal still considered Ethernet?
• Sub panel location question
• Reducing wattage of a portable car heater
• Deutsche Bahn Berlin: can I use a different departure station?
• How can I politely decline a request to join my project by a free rider professor
• Efficiency of Coaxial Rotors vs Single Rotors (and Contrarotating Propellers)
• Mega Man: Powered Up
• Are there any examples of exponential algorithms that use a polynomial-time algorithm for a special case as a subroutine (exponentially many times)?
• Considerations for UK / USA operation
• What mechanism could cause a person not to cast a reflection?
• Is there a commonly used expression for adjusting a training or form of support to a person's specific situation and needs?

more hot questions Question feed Subscribe to RSS Question feed

To subscribe to this RSS feed, copy and paste this URL into your RSS reader.