Answer:
The given expression is
= 3.3125
Step-by-step explanation:
The given expression is
= 3.3125
Answer: 1. inversely 2. 4,000 3. direct 4. 35
Step-by-step explanation:
In order to multiply a matrix by another matrix, we multiply the rows in the first matrix by the columns in the other matrix (How this is done is shown below)
To determine the pairs of matrices that AB=BA, we will determine AB and BA for each of the options below.
For the first option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-2\times5)+(1\times3)&(-2\times0)+(1\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-10+3&0+2&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&-7&2&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-2%5Ctimes5%29%2B%281%5Ctimes3%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-10%2B3%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-7%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-2)&(5\times0)+(0\times 1)&(3\times1)+(2\times-2)&(3\times0)+(1\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-4&0+2&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&-1&2&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-2%29%26%285%5Ctimes0%29%2B%280%5Ctimes%201%29%26%283%5Ctimes1%29%2B%282%5Ctimes-2%29%26%283%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-4%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
∴ AB≠BA
For the second option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-1\times3)+(2\times6)&(-1\times0)+(2\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-3+12&0+-6&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-1%5Ctimes3%29%2B%282%5Ctimes6%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-3%2B12%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-1)&(3\times0)+(0\times 2)&(6\times1)+(-3\times-1)&(6\times0)+(-3\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+3&0+-6&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-1%29%26%283%5Ctimes0%29%2B%280%5Ctimes%202%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-1%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B3%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here AB = BA
For the third option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-1\times5)+(2\times3)&(-1\times0)+(2\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-5+6&0+4&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-1%5Ctimes5%29%2B%282%5Ctimes3%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-5%2B6%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-1)&(5\times0)+(0\times 2)&(3\times1)+(2\times-1)&(3\times0)+(2\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-2&0+4&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-1%29%26%285%5Ctimes0%29%2B%280%5Ctimes%202%29%26%283%5Ctimes1%29%2B%282%5Ctimes-1%29%26%283%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-2%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here also, AB=BA
For the fourth option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-2\times3)+(1\times6)&(-2\times0)+(1\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-6+6&0+-3&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&0&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-2%5Ctimes3%29%2B%281%5Ctimes6%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-6%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%260%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-2)&(3\times0)+(0\times 1)&(6\times1)+(-3\times-2)&(6\times0)+(-3\times1)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+6&0+-3&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&12&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-2%29%26%283%5Ctimes0%29%2B%280%5Ctimes%201%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-2%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes1%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%2612%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here, AB≠BA
Hence, it is only in the second and third options that AB = BA
and ![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5DB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Learn more on matrices multiplication here: brainly.com/question/12755004
Answer:
4
Step-by-step explanation:
if you grab 4, then you might get one of 2 colors and 2 of the same color. If you grab 3 or 2, you could get all different colors.
1 1/2 I think is the answer