All categories

3 years ago

Which expression gives the determinant of the matrix

Mathematics

2 answers:

svp [43]3 years ago

5 0

For 2 by 2 matrices, you can use the formula (ad-bc) to find the determinant of the matrix.

BartSMP [9]3 years ago

3 0

If the matrix is of 2 by 2 then we can find the determinant of the matrix.

$\begin{bmatrix}a & b\\ c & d\end{bmatrix}$

Then (ad - bc ) gives you the determinant of the matrix.

For example,

$\begin{bmatrix} 2 & 4\\ 1 & -2 \end{bmatrix}$

= (2)(-2) - (1)(4)

= - 4 - 4

$\begin{bmatrix} 2 & 4\\ 1 & -2 \end{bmatrix}$ = -8

You might be interested in

Given that point U is the circumcenter of , which segments are congruent?

aleksklad [387]

How are we supposed to answer that question. When we can't see the segments?

7 0

3 years ago

Let $a$ and $b$ be nonzero real numbers such that

algol [13]

<h3>Answer: -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

4 0

1 year ago

Jessica is asked to write a quadratic equation to represent a function that goes through the point (8, –11) and has a vertex at

Kitty [74]

Answer: c

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

suppose that you plan on taking a summer job selling magazines subscriptions . the magazine company will help you pay $0.75 for

alina1380 [7]

<u>Answer:</u>

Money earned by selling 175 magazine subscriptions will be 3176.25

<u>Solution: </u>

Given that you are planning to take a summer job selling magazine subscription.

For first subscription, magazine company will help you to pay $0.75

For each additional subscription sold, magazine company will pay you $0.20 more than what was paid for previous subscription.

So for second subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 1

And for third subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 2

Generalizing for nth subscription we get

Payments for nth subscription = 0.75 + 0.20(n-1)

so here we can see that arithmetic sequence is formed, having first term

$a_1 = 0.75$ and common difference = d = 0.20

We need to determine sum of above arithmetic sequence for n = 175

<u><em>Formula for sum of arithmetic sequence is as follows </em></u>

$\mathrm{S}_{\mathrm{n}}=\frac{n}{2}[2 a+(n-1) d]$

In our case n = 175, a = 0.75, d = 0.20

$\begin{array}{l}{=>\mathrm{S}_{175}=\frac{175}{2}[(2 \times 0.75)+(175-1) 0.20]} \\\\ {=>\mathrm{S}_{175}=\frac{175}{2}[1.5+(174 \times 0.20)]} \\\\ {\Rightarrow \mathrm{S}_{175}=\frac{175}{2} \times 36.3=3176.25}\end{array}$

Hence money earn by selling 175 magazine subscriptions will be 3176.25

6 0

3 years ago

John has 6 boxes of apples each box holds 12 apples. If 4 of the boxes r full and 2 r half full how many apples does John have??

olga55 [171]

Each box holds 12 apples
He has 6 boxes : 4 are full, 2 are half full

4 with 12, 2 with half of 12 (6)

12*4 + (12/2 * 2)
48 + 6*2
48+12
60

3 0

3 years ago