Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

Emeli Hagan
2021-02-25
Answered

Write the given matrix equation as a system of linear equations without matrices. $\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

You can still ask an expert for help

irwchh

Answered 2021-02-26
Author has **102** answers

Step 1

Given:$\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

Step 2

Now,$\left[\begin{array}{cc}3& 0\\ -3& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}6\\ -7\end{array}\right]$

$\therefore 3x+0\cdot y=6\text{}\text{}\text{}\text{}\text{}\text{}\text{}(1)$

$-3x+1y=7\text{}\text{}\text{}\text{}\text{}\text{}\text{}(2)$

From equation (1) , we have

$\Rightarrow 3x=6$

$\Rightarrow x=\frac{6}{3}$

$\Rightarrow x=3$

Putting x=2 in equation (2) , we have

$-3(2)+1y=7$

$\Rightarrow -6+y=7$

$\Rightarrow y=7+6$

$\Rightarrow y=13$

Answer: Therefore the values of x and y are 2 and 13 respectively

Given:

Step 2

Now,

From equation (1) , we have

Putting x=2 in equation (2) , we have

Answer: Therefore the values of x and y are 2 and 13 respectively

Jeffrey Jordon

Answered 2022-01-27
Author has **2313** answers

Answer is given below (on video)

asked 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

asked 2022-06-25

n men and m women are standing in a line (randomly).

Find the expectancy of the number of men that stand beside a women (at least one side - left or right)

Harder question: Now solve it, but they stand in a circle and not a line.

I wanted to use an indicator:

$X=$ number of men standing beside at least one women.

${X}_{i}=1\text{}\text{}\text{}\text{if standing besides a women}\phantom{\rule{0ex}{0ex}}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}0\text{}\text{}\text{}\text{else}$

And so: $E[X]=E[\sum _{i=1}^{n}{X}_{i}]=\sum _{i=1}^{n}E[{X}_{i}]$

the problem is that I am having a time computing what is the probability a random men will stand next to a women (left or right or both)

Find the expectancy of the number of men that stand beside a women (at least one side - left or right)

Harder question: Now solve it, but they stand in a circle and not a line.

I wanted to use an indicator:

$X=$ number of men standing beside at least one women.

${X}_{i}=1\text{}\text{}\text{}\text{if standing besides a women}\phantom{\rule{0ex}{0ex}}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}\text{}0\text{}\text{}\text{}\text{else}$

And so: $E[X]=E[\sum _{i=1}^{n}{X}_{i}]=\sum _{i=1}^{n}E[{X}_{i}]$

the problem is that I am having a time computing what is the probability a random men will stand next to a women (left or right or both)

asked 2022-01-30

What is the conjugate of the complex number $10+3i$ ?

asked 2022-08-10

Find the normal vector N to $\mathbf{r}\mathbf{(}\mathbf{t}\mathbf{)}\mathbf{=}\u27e8\mathbf{t}\mathbf{,}\mathrm{cos}\mathbf{t}\u27e9$ at $t=\frac{9\pi}{4}.$

How do I find this normal vector? So basically I did what the feedback said. I found the derivative of each function in the vector and got.

$(1,-\mathrm{sin}(t))$

Then I got the magnitude:

$\sqrt{1+{\mathrm{sin}}^{2}\left(\frac{9\pi \phantom{\rule{mediummathspace}{0ex}}}{4}\right)}$

Then I divided everything in my vector by that magnitude while putting in

$\frac{9\pi}{4}$

like so:

$\frac{-\mathrm{sin}\left(\frac{9\pi}{4}\right)}{\sqrt{1+{\mathrm{sin}}^{2}\left(\frac{9\pi \phantom{\rule{mediummathspace}{0ex}}}{4}\right)}}$

What my problem? Here's my answer:

$\u27e8\sqrt{\frac{2}{3}},-\frac{\sqrt{3}}{3}\u27e9$

How do I find this normal vector? So basically I did what the feedback said. I found the derivative of each function in the vector and got.

$(1,-\mathrm{sin}(t))$

Then I got the magnitude:

$\sqrt{1+{\mathrm{sin}}^{2}\left(\frac{9\pi \phantom{\rule{mediummathspace}{0ex}}}{4}\right)}$

Then I divided everything in my vector by that magnitude while putting in

$\frac{9\pi}{4}$

like so:

$\frac{-\mathrm{sin}\left(\frac{9\pi}{4}\right)}{\sqrt{1+{\mathrm{sin}}^{2}\left(\frac{9\pi \phantom{\rule{mediummathspace}{0ex}}}{4}\right)}}$

What my problem? Here's my answer:

$\u27e8\sqrt{\frac{2}{3}},-\frac{\sqrt{3}}{3}\u27e9$

asked 2022-02-27

Calculate the value of expresion:

$E\left(x\right)=\frac{{\mathrm{sin}}^{6}x+{\mathrm{cos}}^{6}x}{{\mathrm{sin}}^{4}x+{\mathrm{cos}}^{4}x}$

for$\mathrm{tan}\left(x\right)=2$

for

asked 2022-01-29

Compute $\int \mathrm{sin}\left(x\right)(\frac{1}{\mathrm{cos}\left(x\right)+\mathrm{sin}\left(x\right)}+\frac{1}{\mathrm{cos}\left(x\right)-\mathrm{sin}\left(x\right)})dx$