in-exercises-19-assume-that-the-matrices-are-partitioned-conformably-for-block-multiplication-comp-4

Question

In Exercises 1–9, assume that the matrices are partitioned conformably for block multiplication. Compute the products shown in Exercises 1–4.
$\left[\begin{array}{rr}{I} & {0} \ {-X} & {I}\end{array}ight]\left[\begin{array}{ll}{A} & {B} \ {C} & {D}\end{array}ight]$

Runpeng Li · Accepted Answer

Okay, so for problem for again we have to partition matrices, negative eggs, and I and a B C D. All right again we apply the matrix multiplication rule. So this will be I times a So that&#x27;s just a and zero times See said that zero and I temps piece Oh, that&#x27;s B. And there were times stay just e So on the second row we have connective x times, eh? Plus, I&#x27;m seeing just a C and second entry will be negative. X times be Plus, here we have items D so it&#x27;s just d and here&#x27;s our

Jack Chen · Answer

Okay. So since the since these two mattresses are petitioned conform of Lee So we can just direct used the metrics modification to find out a result. And the music case I means the identity a matrix and we omit the dimension because yes, I said it before They are petitioning conform obl e So we have the first injury. Where have I times a prized zero times. See Nephila second engine. We have items be past the old times d and we have e times A plus I can see in the e times pre processed items at past items D so you can simplify this? We have a e times a process e he times beep rosti. So this is the result to this problem?

Runpeng Li · Answer

Okay, so for problem, too. We need to consider the matrix product up to partition Matrix Bureau F and A B C D. Okay, so the only thing we need to do is just a matrix matrix multiplication role. And but the thing we need to be careful or here is, um, the thing that we need to be care Boyce is the the order off the off the different partitions? Because we know, in general, the mutual submission body modification. It&#x27;s not a community, so Okay, so for problem, too, we need to consider the Matrix port upped up to partition me shakes here we can first have e times, eh? Zero times, See, so that zero. So just stay anytime, Say, don&#x27;t write it as that eight times e because that&#x27;s probably wrong just in general, because anytime say it&#x27;s not it&#x27;s same as the Daytime Z, and also we have your time speed on the second entry and have time see and have times deep for the last central F and A B C D. Okay, so the only thing we need to do is just a matrix matrix multiplication role, and but the thing we need to be cared for Here is, um the thing that we need to be careful voice is the the order off the off the different partitions? Because we know, in general the mutual submission body modification. It&#x27;s not a community, so

Jack Chen · Answer

because in this program we can just directly use the rules for the magics multiplication. And we don&#x27;t need to care about the dimension because the dimensions arm aged Okay, I&#x27;m so for the first interview have zero times w plus i times why? For second trees zero times x plus i times the the third in trim of the items W plus zero times Why last in trilby I Times X plus zero times e and the Miss case I means identity sub matrix. So in the end, we have the results. Why time on y and Z w in the eggs Since off these zeros are cancels and the we can you know this I because I z identity?

Runpeng Li · Answer

All right, so four problem. 14. The game we don&#x27;t given three by three matrix. That is one negative to a negative six. And And 037 and one connected to and five and or the vector we&#x27;ll give it. Here is 11 next, five and nine. So to find again to find out, um, whether whether bees Adelina combination off objectors formed by the columns of this matrix. So the thing we need to consider against the the augmented matrix hey, admitted to be And so this is actually we need to consider the linear system, Max. It would be. And we want to find whether this system is consistent and we consider such a such undocumented matrix. And we apply culture animation to find a role. Reduce station form right down the final form here. So this will be 100 2 45 over 33 and the second rule would be 010 and 41 over 33. Start negative. 41 negative. 41 over 33. And the last role will be there was everyone and negative to over 11. Okay, so, bye, Elise will reduce lesion form. We say X is x one x two Next three them from the last rule we know X tree extra A is next to over 11 and next to we&#x27;ll be on the second row. How just we write a three here. So that&#x27;s next x three will be connective till 11. X x x two will be in negative 41 over 33. So I did four over 33. So negative for 41 over 33 And next one from the first row. We know it is. Ah, Wei. Yeah, yeah, he said to 45 over 33. And so this is our vector X. So under this circumstance, we can have the Lena combination off be in terms of column self matrix.

Rachel Mcmahon · Answer

right in this video. We&#x27;re gonna take a look at some scaler multiplication for, um, this matrix deep. We are asked to find 100 d s. So that just means that we need to multiply each element in the Matrix tea by 100. So our first elements gonna be 18 times 100. The next one&#x27;s gonna be eight turns 107 times, 112 times, 114 times 100 or times 100 13 times 100 6 times 100 and 21 times 100 scaler multiplication.

Problem

Find formulas for X, Y, and Z in terms of A, B, a…

Problem 4 Easy Difficulty

In Exercises 1–9, assume that the matrices are partitioned conformably for block multiplication. Compute the products shown in Exercises 1–4.
$\left[\begin{array}{rr}{I} & {0} \\ {-X} & {I}\end{array}\right]\left[\begin{array}{ll}{A} & {B} \\ {C} & {D}\end{array}\right]$

Answer

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Caleb E.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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Linear Algebra and Its Applications

Anna Marie V.

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Caleb E.

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Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Anna Marie V.

Kayleah T.

Caleb E.

Kristen K.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications