Answer:
![\left[\begin{array}{cc}2&8\\5&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%268%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The <em>transpose of a matrix </em>
is one where you swap the column and row index for every entry of some original matrix 
. Let's go through our first matrix row by row and swap the indices to construct this new matrix. Note that entries with the same index for row and column will stay fixed. Here I'll use the notation 
and 
to refer to the entry in the i-th row and the j-th column of the matrices 
and 
respectively:
Constructing the matrix from those entries gives us
![P^T=\left[\begin{array}{cc}2&8\\5&1\end{array}\right]](https://tex.z-dn.net/?f=P%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%268%5C%5C5%261%5Cend%7Barray%7D%5Cright%5D)
which is option a. from the list.
Another interesting quality of the transpose is that we can geometrically represent it as a reflection over the line traced out by all of the entries where the row and column index are equal. In this example, reflecting over the line traced from 2 to 1 gives us our transpose. For another example of this, see the attached image!
Answer:
The value of the 5 in 50.89 is 100 times the value of the 5 in 261.58
Step-by-step explanation:
The 5 in 50.89 is in the 10's place
The 5 in 261.58 is in the 1/10's place
1/10(100) = 10
Answer:
extra-large
Step-by-step explanation:
Answer:
11 + 2x
Step-by-step explanation:
First you will want to separate like variables, so (6, 5) and then (-2x, 4x)
Then you will use the signs to do the math. You can move everything to help visualize the solution easier.
6+5+4x-2x
6+5 = 11
4x-2x = 2x
Because you cannot add or subtract a variable with a non variable, and both numbers are positive you end up with
11 + 2x
Answer:
x : 4
Step-by-step explanation:
The ratio of a number and 4 into algebraic phrase ;
Let the number = x
Expressing the number and 4 as a ratio in algebraic phrase will be written as :
Number : 4
x : 4
