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lbvjy [14]
3 years ago
5

Suppose that A is nonsingular. Prove that its inverse A-1 is unique. [Hint: Show that if there exists two matrices, B and C, suc

h that BA = I and AC −=I, then necessarily B =C.]
Mathematics
1 answer:
Bogdan [553]3 years ago
4 0

Answer with Step-by-step explanation:

Let A is non-singular

\mid A\mid\neq 0

We have to prove that A^{-1} is unique.

Suppose B and C are inverse of A such that

BA=I and AC=I

By using property AA^{-1}=A^{-1}A=I

C=C

(BA)C=B(AC)

I\cdot C=B\cdot I

C=B

Hence, the inverse of A is unique.

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In the diagram below what is the relationship between the number of rectangles in the perimeter of the figure they form?
Wewaii [24]

Answer:

the correct answer is the third one.  (1, 16), (2, 20), (3, 24)

Step-by-step explanation:

A perimeter is a path that surrounds a two-dimensional shape.

In the first case, 1 rectangle, the perimeter is the sum of all the sides:

Perimeter = 6 + 2 + 6 + 2 = 16

In the second case, 2 rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 6 + 2 + 2 = 20

In the third case, three rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 2 + 6 + 2 + 2 + 2 = 24

In none of the cases, you take into consideration the interal sides. Just the external sides, so the correct answer is the third one.

8 0
3 years ago
A shopper buys 3 notebook for $5 each the percent of sales tax is 8% how much is the total sale
Vlad1618 [11]
All you have to do is 3×5=15
then 8÷8=1 so 16 dollars
6 0
3 years ago
Layla and Bobby want to make 10 potholders each. If it takes one-eighth of a yard to make each potholder, how much total fabric
Yuki888 [10]
Answer: 1.25
explanation: you multiply the amount of fabric used for one by the amount of potholders
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4 0
3 years ago
A basketball team played 25 games and won 7 more then they lost. How many games did they win and lose
Darya [45]

Answer:

lost = 9 games

and

won = 9 + 7 = 16 games

Step-by-step explanation:

Given that:

Total games played = 25

According to given condition:

lost = x

won = 7 + x ----------- eq1

x + x + 7 = 25

2x = 25 - 7

2x = 18

x = 9

So they lost = 9 games

and won = 9 + 7 = 16 games

i hope it will help you!

7 0
3 years ago
Read 2 more answers
The collection of all input values is the ___ of the function ?
hichkok12 [17]

Answer:

Domain

Step-by-step explanation:

Input Values Form the Domain of the Function

Mathematicians call the set of all input values for a function its domain.

3 0
2 years ago
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