The formulas:

Expand the expression:

Plug the values into the expression:
Answer:
Step-by-step explanation:
for reflection around x-axis.
(x,y)→(x,-y)
so P' is (-7,4)
Answer:
Option C
Step-by-step explanation:
- For the matrix A of order
to be invertible, its determinant must not be equal to zero, |A|
0,
exists if- AC = CA = I, where I is identity matrix.
- The homogeneous equation with coefficient matrix A has a unique solution:
AB = 0, B = 
Thus, B = (0, 0, 0......., 0) is a unique solution
2. The non - homogeneous equation system with coefficient matrix A has a unique solution:
For an equation- AY = D
Y =
is a unique solution
3. Every non homogeneous equation with coefficient matrix A is not consistent as:
For an equation- AY = D, has a solution.l Thus coefficient matrix is inconsistent whereas augmented matrix is.
4. Rank of matrix A = n, Thus the column space of A is 
5. Since, column space of A =
, thus x→xA is one-to-one
A ton is 2,000 pounds so multiply 2,000 x 18
2,000 x 18 = 36,000 pounds, now add the 42 pounds to the 36,000
36,000 + 42 = 36,042 pounds. Now divide 36,042 by 3
36,042 ÷ 3 = 12,014
Your answer is 12,014 pounds
If you need your answer in tons it's 6.007 tons
Calculations for pounds to tons
12,014 ÷ 2,000 = 6.007
Hope this helps. :)