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V I h Ihe correcl answrer below 1 1 peliet [0 use heta Itbullur (0 UIL 1 3 3 3 3 3 j...

Question

V I h Ihe correcl answrer below 1 1 peliet [0 use heta Itbullur (0 UIL 1 3 3 3 3 3 j

V I h Ihe correcl answrer below 1 1 peliet [0 use heta Itbullur (0 UIL 1 3 3 3 3 3 j



Answers

Use the matrix below to perform the indicated operation on the given matrix. $$B=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array}\right]$$ $$B^{3}$$

Okay, we're asking to find the norm of the. Now the norm of V is the magnitude of the So it's really, if you consider that these are components, um they would form triangles. And we're really looking for our high pot news because that is going to be the distance Between 00 and the point that we are going to. Okay, so for a we will be finding the magnitude of the by taking the square root of one squared plus negative one squared. And obviously it doesn't matter if we bring our negative in because it is going to get squared. Um but that will end up being squared too. So when I write my problems out, I will put the negatives in there. Um But often on my calculator, I don't, if you forget apprentices, you're taking a negative of a one squared, which can be an issue. So just um, I would say in your calculator because you know, you're squaring it, just put the positive in there and so you don't make any um silly mistakes. So this guy is the square root of negative one squared plus seven squared, which is square at a 50 50 is made of 25 2. So we can take the square root of 25 put a five in front five square too. Now notice our next um vector has three components, and if you have a hypothesis of two of them and you square it and you add it to the third squared and take that square root, um that also works. So what happens is you can again just take the some of your squares, it works fine. So if you're finding the magnitude, we can just do a negative one squared plus a two squared plus a forest squared, and then take the square root of that. So let's say we have 14 16, So that is going to be 21, so square root of 21 and our last one also have the three components. So we will do a three squared a two squared in a one squared, so that's nine plus four plus one. So that will be the square root of 14.

We want to use a calculator to find the inverse to this matrix. So I'm using the desk most uh that's most matrix calculator. I'm gonna hit a new matrix and choose four by four and then input the elements 3100 1310 0131 0013. It enters so that it is stored and then you choose matrix A. And hit the inverse button and you can round those decimals or you can turn them to fractions if you wish. So it's 21 55th negative. 8 50 53 55th negative one 55th negative eight 55th 24 55th negative 9 50 53 50 53 55th negative nine 55th 24 50 58 55th negative 1 50 53 55th negative. Eight 55th 21 55th yeah. Mhm.

In the question we have to verify that the micro Xa into the joint of a as opposed to their joint of a. Into the matrix which is equal to the determinant of a. Now here the matrix given us 23 minus four minus six. Now moving towards the solution like these microbes between my proxy. So they are joined of A will be The metrics with the element -6 -3, four and two. So the A matrix into the joint of a matrix will result in the My tricks with elements 000 zero. Now again we will be finding the determinant of the matrix. A. So 23 minus four minus six. This will result in zero and so the determinant Of my tricks a into the identity matrix which is zero into the identity matrix which is 1001 will result in the matrix with the element 0000 Hence LHs is a call to the Rhs so proof. Thank you.

In the question we have to verify that the micro Xa into the joint of a as opposed to their joint of a. Into the matrix which is equal to the determinant of a. Now here the matrix given us 23 minus four minus six. Now moving towards the solution like these microbes between my proxy. So they are joined of A will be The metrics with the element -6 -3, four and two. So the A matrix into the joint of a matrix will result in the My tricks with elements 000 zero. Now again we will be finding the determinant of the matrix. A. So 23 minus four minus six. This will result in zero and so the determinant Of my tricks a into the identity matrix which is zero into the identity matrix which is 1001 will result in the matrix with the element 0000 Hence LHs is a call to the Rhs so proof. Thank you.


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