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Consider Ihe following matricesFor each ol Ine following matrices, determine Khelner it can be written a5 & linear combination ot tnese malnces 5O, give the lln...

Question

Consider Ihe following matricesFor each ol Ine following matrices, determine Khelner it can be written a5 & linear combination ot tnese malnces 5O, give the llnear combination using the matrix femes above linear combination: ~10Select an answerSelect an answer

Consider Ihe following matrices For each ol Ine following matrices, determine Khelner it can be written a5 & linear combination ot tnese malnces 5O, give the llnear combination using the matrix femes above linear combination: ~10 Select an answer Select an answer



Answers

Determine $A$ c by computing an appropriate linear combination of the column vectors of $A$. $$A=\left[\begin{array}{llll} a & b & c & d \\ e & f & g & h \end{array}\right], \mathbf{c}=\left[\begin{array}{l} x \\ y \\ z \\ w \end{array}\right]$$

So, Asa First metrics, we have the certain that issue ads last for y equals 40 and for a 2nd 1 that it's love ax plus for why you coast through five and we can see for the knocks one that does are one times ah Hoff be Anouar one. We can see that ICO too. 1 to 7, five for five. That's a new Mattrick ce. We can have our words. That's, um, ex loves to Why come through 75 x plus For why ICO soon, right? Also, we can see the knocks for the next metrics. We have one to mine. Oh, salan the Roman on six and minus 30 We can see the first row is the same. So we have a a newly are too. So are two just ecos too Uh, 40 times my notes files and then plasters are too. Now we can see system here It's axe my nose to why he comes from minus seven And also we have many six Why you go through my an insurgent and then three times a second roll Reese my notes 16 you are so new are too and that's equal to one to menace that one. Sorry, that is not a minor. Seven minutes of seven. And those different this'll. So for the second role will have 01 thought because we come to drove by my nose. 16 So we have our system here. That is axe. Oh, so ax last two. Why? Because soon seven Sorry. We need to change your manners here and for the executor road. That is why ICO c five. So for now, we only need to change the first row 210 So the newly first row ico sue the second role Times minus two last stuff for its role. And now we can have all worked. So some axe ico soon, my notary and why you coastal fact wrestle till

So we want to know if this equation is true. So you want to multiply the Matrix to Nick 135 Make sure stay times the quantity of be time. See before home. Eight. Soon. What a multiply. Where to me. So you want to see if that is the same as the other side of the equation? So you want to multiply? This'll part first. Okay, so this is gonna be another two by two matrix when you multiply it out will be negative. Four times three will be negative. 12 and then negative for I mean And then one times negative one will be negative. One. So negative 12 plus Make it. If one would be making a 13 and you multiply with the second column. Negative. Four times twos. Negative eight. And then plus one times two would be chosen at those together Will be negative. Six. They're going to do the second row. Eight times three is 24 0 time thinking of one will be zero. So this will be 24 and then negative eight times two of 16 plus zero times to be 16. I mean, zero times 20 and then When you add together, we 16 and then you're gonna multiply this matrix wave matrix A. I'm gonna dio this road times this calm again. It will also be a two by two matrix. So two tons negative 13 is negative. 26 negative one times 24 7 Dated 24. When you add those two numbers together, it will be negative. 50. My gonna multiply it with next column two times negative six. It's negative. 12 Negative one times 16 will be negative. 16. When you have those two, it would be negative. 28. They're gonna move with the second part. The second room three times Negative 13 negative 39 5 times 24 is 120. So when you add those two together, it will be 81 three times negative. Six is negative. 18 5 times 16 is 80 when combined. Those to be 62. Now we want to see if this is gonna be equal to the quantity of a bee matrix of a B. So that will be to make it one. That's a negative fund. 35 matrix B will be negative for those. That's right. Negative for 18 Cyril. So you want to multiply this first and then you're gonna multiply it with the matrix C? Sorry. That's a three. You try that again? Me to Oh, negative one to All right, So let's multiply this first two times in the forest. Negative eight. Negative. One times AIDS is gonna be native. Eight. So you combine those two, it's gonna be negative. 16. Then you can multiply with the second roll. Two times. One is two negative. One times zero It's Cyril's that that would be it too. They're gonna multiple the second role. Three times. Negative force Negative. 12 5 times eight is 40. When you combine those two, it's gonna be 20 aids. Three tons. One is 35 times zero is Cyril. So it's gonna be three and you want a multiply it. But the next matrix So again, it's gonna be this role multiplied by this first column and it will be a two by two Negus 16 times three is negative. 48 2 times negative. One is thinking too. So you combine those two. It's gonna be negative. 50 being a multiply with the second column Negative 16 times two is negative. 32 2 times two is gonna before. When you combine, that will be negative. 28 28 times three is 84 3/10. NATO one is negative. Three. When you combine that it would be 81. And then you got multiple with the second column 28 times to its 56 3 times to six. When you committed that, it will be 62 little 62. And then now we can see that these two laters are equal.


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