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Luda [366]
3 years ago
13

Let A and B be square matrices. Show that if ABequals=I then A and B are both​ invertible, with Bequals=Upper A Superscript nega

tive 1A−1 and Aequals=Upper B Superscript negative 1B−1.
Mathematics
1 answer:
stich3 [128]3 years ago
5 0

Step-by-step explanation:

Since AB=I, we have

det(A)det(B)=det(AB)=det(I)=1.

This implies that the determinants det(A) and det(B) are not zero.

Hence A,B are invertible matrices: A−1,B−1 exist.

Now we compute

I=BB−1=BIB−1=B(AB)B−1=BAI=BA.since AB=I

Hence we obtain BA=I.

Since AB=I and BA=I, we conclude that B=A−1.

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How do I solve 8760-1353?
posledela

Answer:

7507

Step-by-step explanation:

8760-1253=7507

3 0
3 years ago
Need help with this question
posledela

Answer:

QR = 82.38 to nearest hundredth.

Step-by-step explanation:

As they are similar corresponding sides are in the same ratio.

So MN / QR = LM / QR

13/51 = 21/ QR

`3QR = 51*21

QR = 51*21/13

QR = 82.38

4 0
3 years ago
Please help! I’m very confused on this question. I’m not very good at geometry.
Ahat [919]

Well, to find the perimeter we have to add all of the side lengths, so let's do that:

2x+3 +2x+3 +2x

And we know that this equals 36 so let's solve for x

2x+3+2x+3+2x = 36

6x+6 = 36

6x = 30

x = 5

So we know know that x = 5.

Now all you have to do is plug in the values of x into the lengths

2(5) + 3

= 10+3

= 13 is the length of two of the sides.

2x

= 2(5)

= 10

And 10 is the length of the last side.


8 0
3 years ago
Read 2 more answers
G(t)= t-3 <br> h(x)= 3t-2 <br> find (g-h)(t)
Marina86 [1]

Answer:

g(t) - h(t) = -2t - 1

Step-by-step explanation:

g(t) - h(t) = t-3-3t+2

= -2t -1

6 0
3 years ago
This table represents the number of inches, n, a plant grows after m, months in a new pot.
Yuki888 [10]

Answer: Slope = 5/4

y-intercept = 2

Step-by-step explanation:

We have the table:

Months, m            Plant height in inches, n

0                           2

2                           4.5

4                            7

6                            9.5

We want a linear relationship to represent this table.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case we can select any pair of points, for example, i will choose the first two:

(0, 2) and (2, 4.5)

Then the slope is:

a = (4.5 - 2)/(2 - 0) = (2.5/2) = 1.25 = 5/4

Then our line can be written as:

y = (5/4)*x + b

To find the value of b, we can replace the values of any of the points in the equation, for example, i will use the point (0, 2) or x = 0, y = 2.

2 = (5/4)*0 + b

2 = b

Then our equation is:

y = (5/4)*x + 2.

Slope = 5/4

y-intercept = 2

8 0
3 years ago
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