Answer:
Yes the linear transformation is one to one and it maps a set of real numbers R cubed onto set of real numbers R cubed
Step-by-step explanation:
To show that the linear transformation is one to one, we must show that the columns are linearly independent columns (i.e it must have the trivial solution)
![A = \left[\begin{array}{cccc}1&-2&3&0\\-1&3&-4&0\\-5&-2&9&0\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-2%263%260%5C%5C-1%263%26-4%260%5C%5C-5%26-2%269%260%5Cend%7Barray%7D%5Cright%5D)
For the Augumented matrix A and applying Row Reduction Formula we have that
= ![\left[\begin{array}{cccc}1&-2&3&0\\0&1&-1&0\\0&0&-18&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-2%263%260%5C%5C0%261%26-1%260%5C%5C0%260%26-18%260%5Cend%7Barray%7D%5Cright%5D)
we can deductively see that 
Since the columns are linearly independent, Hence it is a one-to-one transformation and it maps a set of real numbers R cubed onto set of real numbers R cubed
Answer:
a=-22
Step-by-step explanation:
Multiply both sides of the negative equation by (-2) to get the equation:
a-4=13(-2)
then simplify to get:
a-4=-26
then isolate the variable by addig 4 to both sides of the equation to get:
a=-26+4
simplify to get:
a=-22
Answer:
x = 
, y = 2
Step-by-step explanation:
3x + 3y - 7 = 12x + y
6y - 12x - 1 = -45x
(3x - 12x) + (3y - y) = 7
(-12x + 45x) + 6y = 1
-3(-9x + 2y = 7)
33x + 6y = 1
27x - 6y = -21
33x + 6y = 1
60x = -20 -> x = -20/60 = -1/3
-9x + 2y = 7 -> y = 
= 
= 2
The ratio 2 to 6 can be reduced to 1 to 3. That means for every 3 cups of flour there is one cup of sugar.
Answer: 106 yards
Step-by-step explanation: Find the square root of 702.25 which is 26.5, then times 26.5 by 4 to find the perimeter. 106 yards.
