Emily-Jane Bray
2021-01-28
Answered

For each of the following matrices, determine a basis for each of the subspaces R(AT), N(A), R(A), and N(AT):

$A=\left[\begin{array}{cc}3& 4\\ 6& 8\end{array}\right]$

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nitruraviX

Answered 2021-01-29
Author has **101** answers

Step 1

Given:

Step 2

Apply

whose rank is 1

Now,

Apply

Whose rank is 1

For N(A)

Step 3

Jeffrey Jordon

Answered 2022-01-30
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 2022-03-21

Solve the equation $\mathrm{sin}\left(3x\right)\mathrm{cos}\left(x\right)=\frac{2}{3}$ for $x\in [0,\frac{\pi}{2})$ but I could not do it. I tried to develop $\mathrm{sin}\left(3x\right)=\mathrm{sin}(x+x+x)$ and I arrived at the step where the equation becomes $(4{\mathrm{cos}}^{2}\left(x\right)-1)\mathrm{sin}\left(x\right)\mathrm{cos}\left(x\right)=\frac{2}{3}$ and I could not go further !

asked 2022-01-17

How do you simplify $\sqrt{-4}-\sqrt{-25}$ ?

asked 2022-04-24

How to solve $\mathrm{cot}\left(2x\right)=-\frac{7}{6}$ ?

Trying anything at one point, I thought I could rearrange to get$\mathrm{tan}\left(2x\right)$ then apply $\mathrm{arctan}$ and divide by 2 but that doesn't work.

The angle x is supposed to be 69.7 degrees from the solutions I'm working with.

Trying anything at one point, I thought I could rearrange to get

The angle x is supposed to be 69.7 degrees from the solutions I'm working with.

asked 2022-07-07

I'm supposed to implicitly differentiate $\mathrm{sin}(x+y)=2x-2y$. I've already taken the first derivative and got

$(\frac{dy}{dx}+1)\cdot \mathrm{cos}(y+x)=-2(\frac{dy}{dx}-1)$

$(\frac{dy}{dx}+1)\cdot \mathrm{cos}(y+x)=-2(\frac{dy}{dx}-1)$

asked 2022-05-20

Show that $\frac{1+\mathrm{sin}A}{\mathrm{cos}A}+\frac{\mathrm{cos}B}{1-\mathrm{sin}B}=\frac{2\mathrm{sin}A-2\mathrm{sin}B}{\mathrm{sin}(A-B)+\mathrm{cos}A-\mathrm{cos}B}$