What are expressions that are equivalent to 16x + 36

To find them you need to plug them in to solve and then eliminate the following by the pass through method. This can help bring the final answer to the "table" leaving you with the final measure of each described angle.

6 0

3 years ago

Show that W is a subspace of R^3.

musickatia [10]

Answer:

Check the two conditions of Subspace.

Step-by-step explanation:

If W is a Subspace of a vector space, V then it should satisft the following conditions.

1) The zero element should be in W.

Zero element can be different for different vector spaces. For examples, zero vector in $\math{R^2}$ is (0, 0) whereas, zero element in $\math{R^3}$ is (0, 0 ,0).

2) For any two vectors, $w_1$ and $w_2$ in W, $w_1 + w_2$ should also be in W.

That is, it should be closed under addition.

3) For any vector $w_1$ in W and for any scalar, $k$ in V, $kw_1$ should be in W.

That is it should be closed in scalar multiplication.

The conditions are mathematically represented as follows:

1) 0 $\in$ W.

2) If $w_1 \in W; w_2 \in W$ then $w_1 + w_2 \in W$ .

3) $$ \forall k \in V, and \hspace{2mm} \forall w_1 \in W \implies kw_1 \in W$

Here V = $\math{R^3}$ and W = Set of all (x, y, z) such that $x - 2y + 5z = 0$

We check for the conditions one by one.

1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.

i.e., 0 - 2(0) + 5(0) = 0

2) Let us assume $w_1 = (x_1, y_1, z_1)$ and $w_2 = (x_2, y_2, z_2)$ are in W.

That means: $x_1 - 2y_1 + 5z_1 = 0$ and

$x_2 - 2y_2 + 5z_2 = 0$

We should check if the vectors are closed under addition.

Adding the two vectors we get:

$w_1 + w_2 = x_1 + x_2 - 2(y_1 + y_2) + 5(z_1 + z_2)$

$= x_1 + x_2 - 2y_1 - 2y_2 + 5z_1 + 5z_2$

Rearranging these terms we get:

$x_1 - 2y_1 + 5z_1 + x_2 - 2y_2 + 5z_2$

So, the equation becomes, 0 + 0 = 0

So, it s closed under addition.

3) Let k be any scalar in V. And $w_1 = (x, y, z) \in W$

This means $x - 2y + 5z = 0$

$kw_1 = kx - 2ky + 5kz$

Taking k common outside, we get:

$kw_1 = k(x - 2y + 5z) = 0$

The equation becomes k(0) = 0.

So, it is closed under scalar multiplication.

Hence, W is a subspace of $\math{R^3}$ .

7 0

3 years ago

Solve for x show work<br> 3(2x-5)=4x+33

VLD [36.1K]

$\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\$

$\large \purple { \rm{Let's \: solve→}} \\$

$\rm{3(2x-5)=4x+33} \\ \\ \rm {solving \: bracket} \\ \\ \rm{6x - 15= 4x + 33} \\ \\ \rm{arranging \: terms} \\ \\ \rm{6x - 4x = 33 + 15} \\ \\ \rm{2x = 48} \\ \\ \rm{x = \frac{48}{2} } \\ \\ \rm{x = \cancel \frac{48}{2} } \\ \\ \rm{x = 24}$

$\purple{\rule{15mm}{2.9pt}} \red{\rule18mm{2.5pt}} \orange{ \rule18mm{2.5pt}}$

$\sf{\:мѕнαcкεя\: ♪...}$

5 0

2 years ago

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