Answer:
multiply the left side of the constant vector by the inverse matrix
Step-by-step explanation:
The matrix equation ...
AX = B
is solved by left-multiplying by the inverse of A:
A⁻¹AX = A⁻¹B
IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix
X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix
![\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-4%261%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cdfrac%7B1%7D%7B11%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%261%5C%5C3%264%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D9%267%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%265%5Cend%7Barray%7D%5Cright%5D)
The coordinates would be (3, 3).
The slope from R to S is given by
m = (0 - 0)/(-4-1) = 0/-5 = 0
The distance from R to S is 5 units straight across.
This means the slope from T to U will be 0, and it will be a horizontal segment. This means the y-coordinate of U will be 3, since the y-coordinate of T is 3.
The distance from T to U will be 5 as well; -2+5 = 3 for the x-coordinate.
This makes the point (3, 3).
Answer:
2
Step-by-step explanation:
This is a true statement.
Consider two events A and B. We say they are complementary if P(A)+P(B) = 1
This means that either event A or event B must happen, since the "1" represents 100% probability. Having a probability of 100% means absolute certainty.
---------
Example:
A = the event it rains
B = the event it does not rain
P(A) = 0.30 = 30% chance of rain
P(B) = 0.70 = 70% chance it does not rain
P(A)+P(B) = 0.30+0.70 = 1
So this shows the two events are complementary.
