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MakcuM [25]
2 years ago
7

Show that ifAB=IandAC=I, then it follows that B=C. Explain how this proves thatthe inverse of the matrix A is unique.

Mathematics
1 answer:
Anna007 [38]2 years ago
6 0

Answer with Step-by-step explanation:

Suppose that a matrix has two inverses B and C

It is given that AB=I and AC=I

We have to prove that Inverse of matrix is unique

It means B=C

We know that

B=BI where I is identity matrix of any order in which number of rows is equal to number of columns of matrix B.

B=B(AC)

B=(BA)C

Using associative property of matrix

A (BC)=(AB)C

B=IC

Using BA=I

We know that C=IC

Therefore, B=C

Hence, Matrix A has unique inverse .

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10x +1 12x-5 solve for x
dimulka [17.4K]

Answer:

x = 3

Step-by-step explanation:

10x + 1 = 12x - 5

Subtract 1 from each side

10x = 12x - 6

Subtract 12x from each side

-2x = -6

Divided by -2

x = 3

5 0
3 years ago
The table shows the distance Shannon ran over a week.
Sedbober [7]

Answer:

Shannon run 1.5 km more on Friday than on Saturday.

Step-by-step explanation:

From the given table

  • Distance run on Friday = 4/2 = 2 km
  • Distance run on Saturday = 1/2 = 0.5 km

  • In order to run how many more kilometers Shannon run on Friday than on Saturday, we need to subtract the distance run on Saturday from the distance run on Friday.

i.e.

Friday run - Saturday run =  2 - 0.5

                                          = 1.5 km

Thus, Shannon run 1.5 km more on Friday than on Saturday.

8 0
2 years ago
If the measure is 3= 122, then the m6= ?
Vladimir [108]

Yo sup??

m3 and m6 for a supplementary pair therefore

m3+m6=180

122+m6=180

m6=58

Hope this helps

7 0
3 years ago
Tell whether the statement "All integers are rational numbers" is true or false. Explain your choice.
Y_Kistochka [10]

Answer:

True, all integers are rational numbers.

Step-by-step explanation:

Because each integer can be written as n/1 and integers can be positive and negative. For example, 3= 3/1 , 3 is the rational number. But all rational numbers like 1/2 =0.5 are not an integer. (fractions, decimals are not integers.)

6 0
2 years ago
A total of $32,000 is to invested, some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is t
Naya [18.7K]
I think all you do is $32,000 / $8,000 which is $4,000.

Meaning $4,000 will be invested in each investment, I may be wrong though.
7 0
2 years ago
Read 2 more answers
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