If the design is the cube in the second answer then it would have a surface area of 25 cm per face of the cube because to get the surface are you would multiple side by side of a face and then to get the full cubes surface area multiple one faces surface area by six because the cube has six faces and to get the volume you cube the side length of 5cm to get 125cm cubed. Hope this helps.

3 0

3 years ago

In matrix multiplication, such as AB=C, the columns of B form the rows of C. why is this?

Gnesinka [82]

Let's work with 2-by-2 matrices so we're on the same page. The ideas will work for any appropriate matrices.

From the rule of matrix multiplication, we see:
$\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right] = \left[\begin{array}{cc} a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22} b_{22} \end{array}\right]$
As you noted, we see the columns of B contributing to the rows of C. The question is, why would we ever have defined matrix multiplication this way?

Here's a nontraditional way of feeling this connection. We can define matrix multiplication as "adding multiplication tables." A multiplication table is made by starting with a column and a row. For example,
$\begin{array}{ccc} {} & 1 & 2 \\ 1 & {} & {} \\ 2 & {} & {} \end{array}$
We then fill this table in by multiplying the row and column entries:
$\begin{array}{ccc} {} & [1] & [2] \\ 1| &1 & 2 \\ 2| & 2 &4 \end{array}$
It's then reasonable to say that given two matrices A and B, we can construct multiplication tables by taking the columns of A and pairing them with the rows of B:
$\left[\begin{array}{cc}a_{11} & a_{12} \\a_{21} & a_{22} \end{array}\right] \left[\begin{array}{cc}b_{11} & b_{12} \\b_{21} & b_{22} \end{array}\right]$

$= \begin{array}{cc} {} & \left[\begin{array}{cc} b_{11} & b_{12}\end{array} \right]\\ \left[\begin{array}{c} a_{11} \\ a_{21} \end{array} \right] \end{array} +\begin{array}{cc} {} & \left[\begin{array}{cc} b_{21} & b_{22}\end{array} \right]\\ \left[\begin{array}{c} a_{12} \\ a_{22} \end{array} \right] \end{array}$

$= \left[\begin{array}{cc} a_{11} b_{11} & a_{11} b_{12} \\ a_{21} b_{11} & a_{21} b_{12} \end{array} \right] + \left[\begin{array}{cc} a_{12} b_{21} & a_{12} b_{22} \\ a_{22} b_{21} & a_{22} b_{22} \end{array} \right]$

Adding these matrices together, we get the exact same expression as the traditional definition.

5 0

3 years ago

Is it similar to BAK??

yaroslaw [1]

Answer:

Step-by-step explanation:

If we add up numbers in one line segment like 15+25 and 10+6 we do not get multiples so the triangle GYK is not similar to BAK

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4 0

3 years ago

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What will be the answer for 9÷3(2+1)?​

What will be the answer for 9÷3(2+1)?