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grandymaker [24]
1 year ago
13

10. (a) Consider the following matrices: A = ( 2 ) B = (3) and C = (-3) w = Find the det(A). [1] (ii) Is the matrix A singular?

Justify your answer. [1] (iii) Suppose the AB = C. Determine the values of x and y. [3] (iv) Is it possible to find the matrix product BA? State why or why not. [2]

Mathematics
1 answer:
Viefleur [7K]1 year ago
6 0

i) We have to find the determinant of A.

We can do this as:

\det(A)=|\begin{bmatrix}{3} & {6} \\ {1} & {-2}\end{bmatrix}|=3*(-2)-6*1=-6-6=-12

ii) We have to find if the matrix A is singular.

Singular matrix have determinant equal to 0.

This is not the case for A, as its determinant is -12. Then, A is not a singular matrix.

iii) We have to find the values of x and y so that AB = C.

We have to write the matrix multiplication and we will obtain a system of linear equations:

We can now solve the system of equations by adding 3 times the second equation to the first equation:

\begin{gathered} 3(x-2y)+(3x+6y)=3(-3)+(-3) \\ 3x-6y+3x+6y=-9-3 \\ 6x+0y=-12 \\ x=\frac{-12}{6} \\ x=-2 \end{gathered}

We can now use the second equation to find the value of y:

\begin{gathered} x-2y=-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{-2+3}{2} \\ y=\frac{1}{2} \end{gathered}

The values are x = -2 and y = 1/2.

iv) When we want to multiply two matrices, the required condition is that the number of columns of the matrix on the left is equal the number of rows of the matrix on the right.

In the case of A(2x2) and B(2x1), when we do A*B this condition is satisfied.

But when we try to multiply BA, the number of columns of B is not equal to the number of rows of A, so the matrix mulitplication is not possible.

Answer:

i) det(A) = -12

ii) A is not singular because singular matrices have determinant equal to zero.

iii) x = -2 and y = 1/2.

iv) Is not possible because the number of columns of the first matrix has to be equal to the number of rows of the second matrix.

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The answer is 35 degrees, but I am unsure of the process in order to get to that answer.
hammer [34]

Answer:

Step-by-step explanation:

Hello There!

So first things first

we need to find the measure of ∠ABD

If you didn´t know the sum of the triangle angles is 180

so to find ∠ABD we subtract the given angles ( 30 and 25) from 180

180-25-30=125

so angle ∠125

Now lets find ∠DBC

∠ABD and ∠ DBC are supplementary angles so the sum of the two angles is 180

So to find ∠DBC we subtract 125 from 180

180-125=55

so ∠DBC = 55

Now we can find the measure of ∠BDC

remember like stated before the sum of all of the angles in a triangle is 180

So to find the measure of ∠BDC we subtract the given angles from 180

180-90-55=35

so we could conclude that ∠BDC = 35

Other ways to solve for ∠DBC:

angle DBC is an exterior angle of ΔABD

the measure of an exterior angle is equal to the sum of the opposite interior angles

so basically ∠DBC = ∠ADB + ∠BAD

30+25=55 so ∠DBC = 55

Other ways to find angle BDC:

Having found the measure of ∠DBA and the other opposite angle we could find ∠BDC

Like stated before the measure of an exterior angle is equal to the sum of the opposite interior angles

basically ∠DBA = ∠BDC + ∠BCA

we have the measures of ∠BCA and ∠DBA so we plug in the values

125=∠BDC+90

isolate the variable by subtracting each side by 90

125-90=35

we´re left with

∠BDC=35

I hope this helps and if you have anymore questions, feel free to ask! :)

4 0
3 years ago
Read 2 more answers
Enter the correct answer in the box.
Agata [3.3K]

3x^3 + 7x - 26 + x + 2

= 3x^3 + 8x - 24  answer

8 0
3 years ago
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Please help ASAP! All questions.
natka813 [3]

Answer:

I think i don't really know its been awhile for me.

Step-by-step explanation:

But i think you do 2 x 10 and what ever you get from that you multiply by 5 and what get from that you divide by 24.

I may not be right.

So please don't hate i tried.

4 0
3 years ago
4ln x -8=12 its giving me other equations
kogti [31]

The solution of the given logarithmic equation is x = 28.1

<h3>How to solve the logarithmic equation?</h3>

Here we have the logarithmic equation:

4*ln(x - 8) = 12

And we want to solve this for x.

Remember the relations:

ln(e^x) = x\\e^{ln(x)} = x

First, we divide both sides by 4:

ln(x - 8) = 12/4 = 3

Then, if we apply the exponential equation to both sides of our equation, we get:

e^{ln(x - 8)} = e^{3}\\\\x - 8 = e^3\\\\x = e^3 + 8 = 28.1

If you want to learn more about logarithmic equations:

brainly.com/question/236421

#SPJ1

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IgorLugansk [536]

Answer:

10.35 miles in 1 hout

Step-by-step explanation:

I'm Sorry if this wrong.

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