Question

1. decide whether each of the following is true or false, and circle the correct answer. (1 point each)

a. a system of linear equations could have exactly two solutions. true / false
b. a system of linear equations could have an infinite number of solutions. true / false
c. if a and b are matrices, then ab is always equal to ba. true / false
d. if f and g are functions, then (f∘g)(x) is always equal to (g∘f)(x). true / false

Explanation:

Step1: Recall linear - equations solution property

A system of linear equations can have 0, 1, or infinitely many solutions. It cannot have exactly two solutions.

Step2: Recall linear - equations solution case

If the lines representing the linear equations are coincident, the system has infinitely many solutions.

Step3: Recall matrix - multiplication property

Matrix multiplication is not commutative in general. That is, for matrices \(A\) and \(B\), \(AB
eq BA\) in most cases.

Step4: Recall function - composition property

Function composition is not commutative. That is, \((f\circ g)(x)
eq(g\circ f)(x)\) in general.

Answer:

a. False
b. True
c. False
d. False