Answer the following statement(s) true (T) or false (F)
1. A system of two linear equations has exactly one solution.
2. If three vertices of a parallelogram are (0, 0), (2, 0) and (5, 4), then the fourth vertex is (7, 4).
3. If three of the vertices of a rectangle are (-a, 0), (a, 0) and (-a, b), then the fourth vertex is (a,-b).
1. False—It may also have no solution or infinitely many solutions.
2. True
3. False—The fourth vertex is at (a, b).
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Given matrices A = 
, B = 
, and C = 
, decide if the statement is true or false.A(B + C) = AB + AC
A. True B. False
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. 5x - y + z = 8 7x + y + z = 6
A. {(
z + 
, 
z, z)}
B. {(- 
z + 
, 
z - 
, z)}
C. ?
D. {(-z + 3, 4z + 7, z)}
Given f(x) and g(x), find the indicated composition.f(x) = x2 + 4; g(x) = 
Find (f ? g)(x).
A. (f ? g)(x) = x2 + 18x + 85
B. (f ? g)(x) = x2 + 13
C. (f ? g)(x) = 
D. (f ? g)(x) = x + 13
Indicate whether the statement is true always, sometimes, or never.The product of two imaginary numbers is a real number.
A. Always B. Sometimes C. Never