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Xelga [282]
4 years ago
10

Write a 3×3 matrix A which A^2 is diagonal while A is not diagonal ?

Mathematics
1 answer:
LenKa [72]4 years ago
3 0

Consider the matrix

A=\begin{bmatrix}0&1&0\\1&0&0\\0&0&1\end{bmatrix}

Multiplying <em>A</em> by itself has the effect of swapping the first and second rows:

A^2=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}

which is diagonal, while <em>A</em> itself is not.

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Mya and 3 of her friends went out to eat, the total bill was 45.99 they gave her a 20% tip and then split the bill. How much did
Makovka662 [10]

Answer:

Tip Per Person: 2.30 Total Per Person: 13.80

Step-by-step explanation:

The total bill is 48.29. When divided among the 4 friends it equals 13.80

3 0
3 years ago
Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
Verdich [7]

The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

And the accurate root is 3 it can be determined by using rules of the rational root equation.

<h2>Given that,</h2>

Function; \rm f(x) = 3x^3 - 13x^2 -3x + 45

<h3>We have to determine,</h3>

Which of the values shown are potential roots of the given equation?

<h3>According to the question,</h3>

Potential roots of the polynomial are all possible roots of f(x).

\rm f(x) = 3x^3 - 13x^2 -3x + 45

Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

\rm p=\dfrac{All\  the \ positive}{Negative\  factors \ of\  45}

\rm q=\dfrac{All\  the \ positive}{Negative\  factors \ of\  3}

The factor of the term 45 are,

\pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45

And The factor of 3 are,

\pm1, \ \pm3

All the possible roots are,

\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

Now check for all the rational roots which are possible for the given function,

\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0

Therefore, x = 3 is the potential root of the given function.

Hence, The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}.

For more details about Potential roots refer to the link given below.

brainly.com/question/25873992

8 0
2 years ago
Evaluate the expression<br> 5(4)^2\20+9^2
arsen [322]
5 \times  \frac{ 4^{2} }{20} +9^{2} \\ \\ 5 \times  \frac{16}{20} + 9^{2} \\ \\ 5 \times  \frac{16}{20} + 81 \\ \\  \frac{80}{20} + 81 \\ \\ 4 + 81 \\ \\ 85 \\ \\ Answer: \fbox {85}
3 0
3 years ago
What is the scale factor when △RST is dilated to △R'S'T'? What is the value of x?
Flauer [41]
6 / 4.5 = x / 6
x = 6* 6  / 4.5
x = 36/4.5
x = 8

SF = 4.5  / 6 = 0.75

answer
<span>A. Scale factor 0.75, x = 8</span>
7 0
4 years ago
Help please will give brainliest
alex41 [277]
<h2>Answer:</h2>

<u>Cost of basketball sneakers with tax</u> = $96.12

<u>Amount of tax</u> = 8% of cost price

= 8/100 × 96.12

= $7.6896.

<u>Cost of sneakers without tax</u> = $96.12 - $7.6896.

= $88.43.

4 0
3 years ago
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