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Whitepunk [10]
3 years ago
6

Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. [Start 4 By 4 Matrix 1st

Row 1st Column 4 2nd Column 5 3rd Column 7 4st Column 5 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 3 4st Column 8 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 EndMatrix ]
Mathematics
1 answer:
Len [333]3 years ago
4 0

Answer:

Yes, it is invertible

Step-by-step explanation:

We need to find in the matrix determinant is different from zero, since iif it is, that the matrix is invertible.

Let's use co-factor expansion to find the determinant of this 4x4 matrix, using the column that has more zeroes in it as the co-factor, so we reduce the number of determinant calculations for the obtained sub-matrices.We pick the first column for that since it has three zeros!

Then the determinant of this matrix becomes:

4\,*Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] +0+0+0

And the determinant of these 3x3 matrix is very simple because most of the cross multiplications render zero:

Det\left[\begin{array}{ccc}1&4&6\\0&3&8\\0&0&1\end{array}\right] =1 \,(3\,*\,1-0)+4\,(0-0)+6\,(0-0)=3

Therefore, the Det of the initial matrix is : 4 * 3 = 12

and then the matrix is invertible

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zysi [14]

Answer:

The concluding part

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
How many solutions does this linear have y= 5x-1 -15x-3y=3?
musickatia [10]
-15x - 3y = 3

-15x - 3(5x-1) = 3 [input y]
-15x - 15x - 3 = 3 [distribute 3 over 5x and -1]
-30x - 3 = 3 [combine like terms]
-30x = 6 [add 3 to eliminate the negative]
x = \frac{6}{-30} [divide by -30 to get x alone]
x = \frac{1}{-5} [reduce the fraction]

Hopefully this is helpful enough to get you to your answer
4 0
3 years ago
Determine the equation of the parabola whose graph is given below. Write your answer in General Form. A parabola on a coordinate
dimaraw [331]

The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

y = a(x-h)^2 +k

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

Learn more about equation of parabola here brainly.com/question/4061870

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6 0
2 years ago
Round to the underlined place​
alexgriva [62]

Answer:

What is the number that needs to be rounded?

Step-by-step explanation:

4 0
3 years ago
2) Shane puts aside $40 per week for his monthly car payment. He earns $320 per week.
ExtremeBDS [4]

Answer:

12.5%

Step-by-step explanation:

320 divided by 40 = 8

100 divided by 8 = 12.5

100% is 320 dollars, which means that 40 dollars is 1/8 of 320. And 1/8 of 100 is 12.5%

8 0
3 years ago
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