Answer:
If AB = BA = I, then B is inverse of A and vice-versa.
Step-by-step explanation:
Given: AB = BA = I
To find: The relation between matrix A and B.
If AB = BA = I, then B is called the inverse matrix of A and is denoted by
.
In that case, A is said to be invertible.
Also, if B is the inverse of A, then A is also the inverse of B.
Hence, the relation between A and B is that both are inverse of each other.
Should be all real numbers
Answer:
1/5
1. 1/56
2. 1/6
3. 1/65
4. 1/7
5. 1/75
1/8
Step-by-step explanation:
The fractions I gave (1/56, 1/6, 1/65, 1/7, 1/75) are all in between 1/5 and 1/8.
A way to think about this is to add a zero to a denominator of 1/5 and 1/8 and turn them into whole numbers:
1/5 --> 1/50 --> 50
1/8 --> 1/80 --> 80
Then find number between them:
55, 60, 65, 70, 75
Then, turn them into a fraction with a 1 as the numerator and the number as denominators:
1/55, 1/60, 1/65, 1/70, 1/75
This is the process. These numbers are all in between 1/5 and 1/8.
I hope this helps you!
(P.S., I don't think this works with negative numbers, though)
Answer:
![\boxed {z = 6}](https://tex.z-dn.net/?f=%5Cboxed%20%7Bz%20%3D%206%7D)
Step-by-step explanation:
Solve for the value of
:
![\frac{1}{4} = \frac{1}{12} + \frac{1}{z}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B1%7D%7B12%7D%20%2B%20%5Cfrac%7B1%7D%7Bz%7D)
-The variable
cannot equal to
since division by zero is undefined. SO, you multiply both sides by
, which is the least common multiple of
,
, and
:
![3z = 12z \times (\frac{1}{12}) + 12](https://tex.z-dn.net/?f=3z%20%3D%2012z%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B12%7D%29%20%2B%2012)
![3z = z + 12](https://tex.z-dn.net/?f=3z%20%3D%20z%20%2B%2012)
-Take
and subtract it from
:
![3z - z = z - z + 12](https://tex.z-dn.net/?f=3z%20-%20z%20%3D%20z%20-%20z%20%2B%2012)
![2z = 12](https://tex.z-dn.net/?f=2z%20%3D%2012)
-Divide both sides by
:
![\frac{2z}{2} = \frac{12}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2z%7D%7B2%7D%20%3D%20%5Cfrac%7B12%7D%7B2%7D)
![\boxed {z = 6}](https://tex.z-dn.net/?f=%5Cboxed%20%7Bz%20%3D%206%7D)
So, the value of
of
.