(a) True. Suppose A is a not a square matrix, with m rows and n columns. Then A² is not defined, because you can't multiply an m×n matrix by another m×n matrix.
(b) False. As an example, consider the matrices
Then both AB and BA are defined, with
In general, you can multiply any m×n by any n×m matrix.
(c) True. Multiplying a m×n matrix by a n×m matrix always yields a m×m matrix, and multiplying a n×m matrix by a m×n matrix always yields a n×n matrix.
He needs to cut 3/8 off because 3 1/8-2 3/4=3/8.
Answer:
The independent variable is x
Step-by-step explanation:
In the equation y = m x + b
- m is the rate of change ⇒ constant
- b is the initial value ⇒ constant
x is the independent variable because it does not depend on any value
y is the dependent variable because it depends on the value of x
Let us solve the question
∵ 5x + 2y = 150
→ Put it in the form above by subtracting 5x from both sides
∵ 5x - 5x + 2y = 150 - 5x
∴ 2y = 150 - 5x
→ Divide each term by 2 to make the coefficient of y equal 1
∴ y = 75 - 2.5x
∴ y = -2.5x + 75
→ Compare is by the form above
∴ m = -2.5 and b = 75
∴ x is the independent variable (domain)
∴ y is the dependent variable (range)
Answer:
Step-by-step explanation:
10x/5x-2 + 7x-2/5x-2
Here both fractions have same denominator 5x-2
When the denominators are same then we can combine the numerators
we put denominator only once
Now we simplify it
Combine like terms: 10x+7x becomes 17x
There is no common factor for the top and bottom
So we cannot simplify further
Answer:
2n + 5
Step-by-step explanation:
- Twice a number (n): 2n
- Five more than twice a number: 2n + 5
I hope this helps!
