All categories

3 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]3 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 .

You might be interested in

The value of Adam's model railway is $550.

garik1379 [7]

Answer:(c)

Step-by-step explanation:

Given

The initial value of Adam's model is $A_o=\$550$

the value increases exponentially with the rate of $r\%$

Time period $t=5\ years$

Final amount $A=\$736$

Exponential growth is given by

$\Rightarrow A=A_o(1+r)^t$

Putting values

$\Rightarrow 736=550(1+r)^5\\\\\Rightarrow (1+r)^5=1.338$

$\Rightarrow 1+r=1.05999\\\Rightarrow r=0.05999\ or\ 5.99\%\approx 6\%$

Option (c) is correct

6 0

3 years ago

Find the value of variable x. If your answer is not an integer, write it in simplest radical form with the denominator rationali

Otrada [13]

Answer:

the answer is 7

Step-by-step explanation:

angle 30°

x=14/2

x=7

8 0

3 years ago

You are painting the root of a boathouse. You are going to place the base of a ladder 12 feet from the boathouse. How long does

jolli1 [7]

Answer:

37 ft

Step-by-step explanation:

The ladder forms a right triangle as it elan's against the wall of the boat house.

Thus, the length of the ladder can be determined using Pythagorean theorem.

c² = a² + b²

c = length of ladder

a = 35 ft

b = 12 ft

Plug in the values

c² = 35² + 12²

c² = 1,225 + 144

c² = 1,369

c = √1,369

c = 37

Therefore, to reach the roof of the boathouse, the length of the ladder = 37 ft

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20%20%5Cdiv%20%20%5Cfrac%7B1%7D%7B12%7D%20" id="TexFormula1" title="

elena55 [62]

I think it is 6/3 not sure

4 0

3 years ago

Read 2 more answers

HELP, Prove: (cos(x))/(sin(x)tan(x))=cot^2x

Mice21 [21]

Answer:

Steps shown below

Step-by-step explanation:

We will simplify this using definitions and identities. Let's start.

$\frac{cos(x)}{sin(x)tan(x)}$

Using $tanx=\frac{sinx}{cosx}$ , we have:

$\frac{cos(x)}{sin(x)\frac{sin(x)}{cos(x)}}\\=\frac{cos^2(x)}{sin^2(x)}$

Using $cot(x)=\frac{cos(x)}{sin(x)}$ , we have:

$\frac{cos^2(x)}{sin^2(x)}\\=cot^2(x)$

Hence, proved.

7 0

3 years ago

Read 2 more answers