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Mademuasel [1]
3 years ago
14

Arrange the matrices in increasing order of their determinant values.

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
8 0

Answer:

c, a, b

Step-by-step explanation:

Given

See attachment for matrices

(a)

D = \left[\begin{array}{cc}\cos\theta &\sin\theta\\ -\sin\theta& \cos\theta\\\end{array}\right]

The determinant of the matrix is:

|D |= (\cos\theta * \cos\theta - \sin\theta *- \sin\theta)

|D | = \cos^2\theta + \sin^2\theta

Using trigonometry ratio, we have:

|D | = 1

(b)

\left[\begin{array}{ccc}2&0\\0&2\end{array}\right]

The determinant of the matrix is:

|D| = 2 * 2 - 0 * 0

|D| = 4 - 0

|D| = 4

(c)

\left[\begin{array}{ccc}0&i\\-i&0\end{array}\right]

The determinant of the matrix is:

|D| = 0 * 0 -(-i * i)

|D| = 0 +i^2

|D| = i^2

In complex numbers

i^2 = -1

So:

|D| = -1

<em>So, the order of the determinants is: c, a, b</em>

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Inga [223]

Answer:

Carla's suitcase was a better purchase.

Step-by-step explanation:

The complete question is:

Carla and Daniel bought identical suitcases at different stores. Carla's suitcase originally cost $75 and was discounted 19% Daniel's suitcase original cost $85 and was on sale for 20% off the original price. Which suitcase was the cheaper?

Solution:

Cost Price of Carla's suitcase = $75

       Discount% for Carla = 19%

       The amount paid by Carla is,

       

       So, the amount paid by Carla was, $60.75.

Cost Price of Jeana's suitcase = $85

       Discount% for Jeana = 20%

       The amount paid by Jeana is,

       

       So, the amount paid by Jeana was, $68.

Carla's suitcase was a better purchase.

5 0
3 years ago
Division number story with the answer 5/2
jek_recluse [69]

Answer:

I have one below (It's kind of simple though..)

Step-by-step explanation:

Harry Had 5 Potions he made in Potions Class. He would like to share the 5 potions with his 2 friends, Ron and Hermione. How many potions do they each get? Write the equation for how many each person gets in fractional form

(This is a simple one I don't have a complicated one..)

8 0
3 years ago
the low temperature in colton for 5 days were -8 -13 -4 -9 and -16 what was the average low temperature for those 5 days
Andreas93 [3]
The average low temperature is -10.
-8+(-13)+(-4)+(-9)+(-16)= -50/5=-10
3 0
3 years ago
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I hope this helps lol

6 0
3 years ago
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Find the values of x and y so that ABCD will be a parallelogram.
arsen [322]

Given:

Figure of a parallelogram.

To find:

The values of x and y.

Solution:

If two parallel lines intersected by a transversal line, then the alternate interior angles are congruent.

4x=24            (Alternate interior angles)

x=\dfrac{24}{4}

x=6

And,

y-10=32            (Alternate interior angles)

y=32+10

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The value of x is 6 and the value of y is 42.

Therefore, the correct option is C.

3 0
3 years ago
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