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Nata [24]
3 years ago
7

Let U be a square matrix such that Upper U Superscript Upper TUequalsI. Show that det Uequalsplus or minus1. Assume that Upper U

Superscript Upper TUequalsI. Since the desired result is that det Uequalsplus or minus​1, an intermediate step must be found which contains the expression det U. Which of the following can be applied to the assumption Upper U Superscript Upper TUequalsI to achieve the desired​ result? A. det ​(Upper U Superscript Upper T​U)Superscript negative 1equalsdet I B. det ​(Upper U Superscript Upper T​U)equalsI C. ​(Upper U Superscript Upper T​U)Superscript negative 1equalsISuperscript negative 1 D. det ​(Upper U Superscript Upper T​U)equalsdet I Simplify the right side of the equation found in the first step. nothing Which property can be used to simplify the left side of the equation found in the first​ step? Select all that apply.

Mathematics
1 answer:
bogdanovich [222]3 years ago
4 0

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the step by step solution of the given problem.

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What is the value of 4*(-1+2-3+4-3+6-7+....+100) Show your work. [Pls help I am really drowning in work. 50 points + brainliest
KengaRu [80]

Answer:

200

Step-by-step explanation:

We have:

4(-1+2-3+4-5+6-7...+100)

We can rearrange the numbers to obtain:

4((-1-3-5-7-...-99)+(2+4+6...+100))

From the left, we can factor out a negative. So:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

In other words, we want to find the sum of all the odd numbers from 1 to 99.

And the sum of all the even numbers from 2 to 100.

Let's do each one individually:

Odd Terms:

We have:

(1+3+5+7+...+99)

We can use the arithmetic series formula, where:

S=\frac{k}{2}(a+x_k)

Where k is the number of terms, a is the first term, and x_k is the last term.

Since it's all the odd numbers between 1 and 99, there are 50 terms.

Our first term is 1 and our last term is 99. So, the sum of all the odd terms are:

S=\frac{50}{2}(1+99})

Divide the fraction. Add within the parentheses:

S=25(100)

Multiply:

S=2500

So, the sum of all the odd terms is 2500.

Even Terms:

We have:

(2+4+6+...+100)

Again, we can use the above formula.

Our first term is 2, last term is 100. And since it's from 2-100, we have 50 even terms. So:

S=\frac{50}{2}(2+100)

Divide and add:

S=25(102)

Multiply:

S=2550

We originally had:

4(-(1+3+5+7+...+99)+(2+4+6...+100))

Substitute them for their respective sums:

4(-(2500)+2550)

Multiply:

4(-2500+2550)

Add:

=4(50)

Multiply:

=200

So, the sum of our sequence is 200.

And we're done!

Note: I just found a <em>way</em> easier way to do this. We have:

4\cdot(-1+2-3+4-5+6-7+...+100)

Let's group every two terms together. So:

=4((-1+2)+(-3+4)+(-5+6)...+(-99+100))

We can see that they each sum to 1:

=4((1)+(1)+(1)+...+(1))

Since there are 100 terms, we will have 50 pairs, so 50 times 1. So:

=4(50)

Multiply:

=200

Pick which one you want to use! I will suggest this one though...

Edit: Typo

8 0
3 years ago
#19 how do you do the work???!
Semenov [28]

Answer:

x=\frac{1}{3}

Step-by-step explanation:

move the terms with x to the left side of the equation:

add 3x to both sides

3x-1+3x=1

add 3x and 3x

6x-1=1

move all term not containing x to the right side:

add 1 to both sides of the equation

6x=1+1

6x=2

divide each term by 6

\frac{6x}{6}=\frac{2}{6}

x=\frac{2}{6}

simplify the fraction

x=\frac{1}{3}

8 0
3 years ago
Each side of a hexagon is 10 inches longer than the previous side. what is the length of the shortest side of this hexagon if it
MrRa [10]

The length of the shortest side of the hexagon is; 41.833 inches

<h3>How to find the perimeter of a Polygon?</h3>

Let the length of the shortest side of the hexagon be x. Now, a hexagon has six sides and if the next side is 10 inches longer than the previous side, then the length of the six sides are;

x, x + 10, x + 20, x + 30, x + 40, x + 50

Perimeter is given as 401 inches. Thus;

x + x + 10 + x + 20 + x + 30 + x + 40 + x + 50 = 401

6x + 150 = 401

6x = 401 - 150

6x = 251

x = 251/6

x = 41.833 inches

Read more about Polygon Perimeter at; brainly.com/question/14490532

#SPJ1

3 0
2 years ago
The diameter of a circle has endpoints P(–10,–2) and Q(4,6).
Luba_88 [7]
The answer is c. forgive me if i am wrong

7 0
3 years ago
Determine whether the variation between the indicated quantities is direct or inverse. The number of calories in a cheese pizza
-BARSIC- [3]

Answer:

The variance is direct.

Step-by-step explanation:

Since size of the pizza determines the amount of calories.

Let us say that a 2" x4" strip of pizza has 250 calories.

Then a pizza of twice the size (or 4" x 4") will have twice as many calories (500 calories) .

8 0
2 years ago
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