6250 Matrices Sac 2011 Multiple Choice & Short Answer

I would reverse engineer this one. The answers are in the MC. I would create a T matrix, and an S matrix then run the static state app to see what the values are in the second year. The S matrix would be a 2x1 column matrix with both values the same. If you like, you can just multiply T x S. That works as well. Start with 112 - no - that gives 156.8. Next 224 - No - that gives 313.6. Next 400. Yep ... that gives 560 and 240.

Elimination saves time. Make sure they have the correct order for rule 2. D & E are out because they create a matrix with 9 elements, not 6.
Next, look at what the second matrix is doing.
You could put the three into your calculator and quickly see the results - that's trial and error, but it would work.
A - multiplying those two increases the turbo and non turbo
B - Multiplying those two keeps the turbo the same, but reduces the non-turbo to 20% of the original price
C - Keeps the values for turbo the same, and reduces the non-turbo to 80% of the original price. That's a 20% reduction.

rows x columns

App: matrixsimequ ... you will find that the cost of $40 is the same for both phones when the minutes are 33.33.

App: no app ... you have to rearrange these two equations C - 0.6m = 20 & C - 0.3m = 30 ... we can then set them up as simultaneous equations, with 20 and 30 as the C matrix. Note ... when a 'C' is used as a variable, you have to be aware that it doesn't mean that it is the 'C' matrix.

App: no app required.

App: inverse ... on the inverse app, you can see the determinant is ad-bc=0.3 ... but you can add a few lines of your own to make it more complete.

App: transitionmatrix ... you find the steady state is 52.5425 ... out of a total of 64 ... that means that 52.54/64 = 82%

App: transitionmatrix - 2012 is after 2 years ... 2010, 2011, 2012. So ... After 1 season 3.06 are not coaching, and after the second 3.33 are not coaching ... the answers said it was 3.06, but that was after only 1 transition ... The answer has to be 3 because you can't have part people coaching ...

The sum of two numbers is 87 ... x+y=87
Their difference is 27 .... x-y=27
Then setup your simequations.
Elimination. Only two have A (2x2), B(2x1) and C(2x1) in correct sequence
Only A has the coefficients represented by 1. There are no 'zero' values in matrix A

App: no app

App: no app ... you have to use the given equation, so you need to enter your matrices as P, Q & R, and then use the calculator function to multiply Q*P+R ...

App: matrixsimequ - Enter the matrices as A, B and C ... keep track of them ... because the problem uses B and X and b ... lots of different things. Convert it all to x, y, z for the variables, and A, B, C for the matrices. A is the numbers, B is the letters, C is the answers. Run the app - then x, y and z are the answers for b, d & r. This problem is created to confuse you and stop you from using the calculator.

App: inverse

App: inverse. Simply enter the matrix as A, then run the inverse App

Time is critical on these. Recognising patterns speeds up the process.
A ... same numbers top and bottom is always a zero.
Calculator or manual for the rest ...
B = 4, C=9, D=4, E=5

Time is critical for these questions. Write the order of the matrix above each.
Then eliminate one by one.
XY is defined check
Z is a column matrix check
The order of X is 2x2 check
The inverse of x is ... false
The value of 2x is ... check ...

If you got D as your answer, you are naturally doing columns first, then rows. It's always rows x columns.

This is a manual process - much faster that way.
Elimination gets you to E, but you should test it on your calculator to be sure as well.

3x1 is a column matrix. There are only 2 column matrices.
The data should contain the Year 2 student data - 12, 20 and 7.

Year 1 data is 26, 9 and 4. Create a 1 x 3 matrix with these numbers and call it A. Create a 3x1 matrix of the numbers provided 12, 8 and 5. Then multiply AxB to give a single number ... if you multiply a 1x3 matrix by a 3x1 matrix - the product matrix is a single number. 404.

This is based on rules 1 and 2 - defining a matrix and defining the product. play with the numbers. B is a 3x2. X is a square matrix ... so its a 2x2 or 3x3
Trial and error of the given matrix orders would give you :
A x X = B
3x2 2x2 = 3x2 ...

Subtraction of two matrices is easy to do manually, but you could still use your calculator

This is all calculator. Enter the first matrix as A, second as B, third as C.
Run the matrixsimequ app - and it will tell you the answer.

Elimination is the key here. The diagonal is a great place to start.
Eliminate any diagonal that isn't 0.7, 0.8, 0.9. There goes A, B and C.
D says that A has 8% that go to B when there are 20% ... so it must be E ... check the other values.

Manually write the order for both matrices. Use rule 1 to check definition, rule 2 to find product matrix.

a 1x3 row matrix represents the food, the 3x1column matrix represents the costs

Matrix A contains the numbers,Matrix B contains the variables, Matrix C contains the answers
Note : be careful to put a zero where there is no value for x, and 1 for when a coefficient is not there.
Also be wary of negative coefficients.

Elimination is important. Look for wrong values.
Diagonal should be 90% - So C and E are out.
A is out because it says 0.3 instead of 0.03 for Weights to running
D is out because it says 0.05 isteand of 0.03 for Weights to Running
B gets all the values correct.
WARNING ... they always use the 0.3 to 0.03 as a separator.

Algebra is often used to test your manual skills. This is where you drag out your formulae. ad-bc=5
ad is 3a, bc is 2a ... so ... 3a-2a=5 ... so ... a=5

Things to note - if nobody has the gathering in the same place two years in a row - that means there is a zero diagonal (that knocks out B & C). Also, columns must add up to 1. (That knocks out D & E) ... process of elimination makes it A.

A unique solution requires a non-zero determinant. Check the determinant for each equation. ONly the first one has a determinant of zero. So ... 3 out of the 4 will have a determinant, and therefore will have an inverse.

App: no app ... as above, but you need to use the previous quest value as the new value for the state matrix. 15.8 and 10.5. Then again, 16.536 and 10.925 ... to finally come up with 17.2131 and 11.2363 ... rounded off to $11.24

App: no app

The value is 54. The row is 3, and represents the Under 12 players and the column is 2, which indcates Division 2 of the competition.