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2 years ago

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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Step-by-step explanation:

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2 years ago

What does X equal? geometry

Otrada [13]

Answer:

x= 77

Step-by-step explanation:

The angle at 122 degrees is a linear pair with the isosceles triangle, meaning it makes 180 degrees.

180-122= 58 degrees

Since it is an isosceles triangle, the two angles at the bottom are both 58 degrees.

Let's use this info to find the degree at the top.

58+58= 116

There are 180 degrees in a triangle, so subtract 116 degrees we have so far to find the last angle.

180-116= 64 degrees

And since the angle at the top makes 90 degrees, we can subtract 64 degrees to find the smaller angle to the right of the 64 degree angle.

90-64= 26 degrees

And since a triangle has a total of 180 degrees, subtract the 26 degrees from 180.

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Your answer is 77 degrees.

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2 years ago

Does anyone know what the √2.25 is when rewritten as a fraction?

Zinaida [17]

Answer: $\sqrt{\frac{9}{4} }$

Step-by-step explanation:

This is what it is as a mixed number

$\sqrt{2.25}$

= $\sqrt{2\frac{1}{4} }$

= $\sqrt{\frac{9}{4} }$

If you want it written in exponential form it would look like this:

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2 years ago

Read 2 more answers

Is 10/18 in decimal form a terminates or repeating decimal

Oksana_A [137]

Hey there! I'm happy to help!

To write a fraction as a decimal, you simply divide the numerator by the denominator.

10÷18=0.55555.... (the 5s never end!)

We see that the 5s repeat forever. This means that this is a repeating decimal.

Have a wonderful day! :D

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3 years ago

Need help using synthetic division!

viktelen [127]

Answer:

$3x^{2} -3x+8-\frac{9}{x+1}$

Step-by-step explanation:

Since we're dividing the polynomial by $(x+1)$ , we'll be using -1 to start the division.

Before setting the division up, let's list the coefficients of $x$ from descending powers and the constant.

The coefficient of $x^{3}$ is 3

Since we don't see an $x^{2}$ , the coefficient will be 0.

The coefficient of $x$ is 5.

Lastly, the constant, which is the term without the $x$ is -1.

Refer to the attached picture before continuing.

After referring to the picture, we now have the coefficients for the quotient.

The coefficient of $x^{2}$ is 3.

The coefficient of $x$ is -3.

The constant is 8.

Lastly, since the last number is not zero, it's the remainder just like regular division. This can be tricky to remember, but -9 is not the actual remainder.

The remainder is actually $\frac{-9}{x+1}$ .

Now putting all the pieces together, we get:

$3x^{2} -3x+8-\frac{9}{x+1}$

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2 years ago