A matrix with a determinant of zero is called a singular matrix and doesn't have an inverse because it indicates the system of equations it represents doesn't have a unique solution, and the transformation it performs is not reversible.
When a matrix has a determinant of zero (det A = 0), it is classified as a singular matrix and is not invertible. This characteristic implies that the matrix cannot be used to find unique solutions for a set of linear equations because such a matrix corresponds to a system of equations that has either no solution or an infinite number of solutions.
The ability to have an inverse matrix is crucial as it allows us to solve matrix equations and essentially 'undo' the transformations applied by the original matrix.
The reason why a zero determinant indicates the absence of an inverse lies in the mathematics of linear transformations.
A determinant of zero suggests that the transformation associated with the matrix collapses the dimensionality of the space, which means some information about the original vectors is lost, and hence, an inverse operation to recover the original vectors cannot exist.
To further illustrate this, consider the matrix equation AB = I, where A is our original matrix and B is its supposed inverse yielding the identity matrix I. It follows from the properties of determinants that det(AB) = det(A) x det(B).
If det(A) is zero, then the product det(A) x det(B) will also be zero, not equal to 1, which is the determinant of the identity matrix. Therefore, B cannot serve as the inverse of A.
In other words, having a non-zero determinant is a prerequisite for a matrix to have an inverse, as it ensures that the system of equations it represents is solvable and that the matrix transformation is reversible.
Find the slope of the line through the points (x1, y1) and (x2,y2)
Answer:
y2-y1/x2-x1
Step-by-step explanation:
A storage tank at a 24-hour gas station contains 25,000 gallons of gasoline at 8:00 a.m. on Monday. At 8:00 a.m. on Friday of the following week, the amount of gasoline in the tank has decreased to 7000 gallons. What is the average hourly rate of change of gasoline in the tank?
If you study hard, then you can pass the tests.
If you pass the tests, then you can pass the class.
What conclusion can be draw from the statements above?
A) Studying hard will allow you to pass the class.
B) Only students who pass tests study hard.
C) If you have passed the class, you must not have studied very hard.
D) Not passing tests means that you did not study.
Answer:
A) Studying hard will allow you to pass the class.
13) Ms. Dowd gave each student 6 liters of water to perform an experiment. Before starting the experiment, students had to verify the volume of water they received by taking three different measurements. Which of the following was the most precise measurement Ms. Dowd received? *
A) 5.9
B) 6.045
C) 6.0014
D) 6.12
Solve for q.
s = 4p + 4q
I'm thinking q= s - 4p
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4
what is the answer to this 5+5x=-2x+5=?
5+5x=-2x+5
Isolate the x. Add 2x to both sides, and subtract 5 from both sides
5 (-5) + 5x (+2x) = -2x (+2x) + 5 (-5)
5x + 2x = 5 - 5
8x = 0
Isolate the x. Divide 8 from both sides
8x/8 = 0/8
x = 0
0 is your answer
hope this helps
A car travels 83 7/10 miles on 2 1/4 gallons of fuel. Which is the best estimate of the number of miles the car travels on one gallon of fuel
round miles up to 84
round gallons down to 2
and divide
84 /2 = 42 miles per gallon ( estimate)
What is the number in scientific notation? 409,200,000,000
What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?
Help me with this please
Problem page the sum of two numbers is 56 . the smaller number is 16 less than the larger number. what are the numbers?
The sum of the angle measures of a polygon with n sides is 1260. find n.
The sum of the angle measures of a polygon with 9 sides is 1260.
What is Angle Sum property?To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
As, the sum of the interior angles
(x - 2) x 180 where x is number of sides.
Here, the angle sum for n side is 1260.
So, (n -2) 180 = 1260
n -2 = 1260 / 180
n - 2 = 7
n= 7+2
n= 9 sides
Thus, the polygon have 9 sides.
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How to find the length of a line in a right triangle with 1 angle and the hypotenuse?
The data value x exists in two data sets: A and B. The mean is equal for both data sets. If the standard deviation for set A is greater than the standard deviation for set B, which is true for zx for set A?
Answer:
answer is B
it is less than Zx for set B
Step-by-step explanation:
Answer:
the second one
Step-by-step explanation:
An isosceles triangle has two sides of equal length. The third side is 5 less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm, what is the length of the third side? Explain how you would define a variable for this problem.
To find the length of the third side, we can set up an equation using variables. Solving the equation will give us the length of the third side.
Explanation:To solve this problem, we can define variables to represent the lengths of the two equal sides of the isosceles triangle. Let's say the length of each equal side is x. The third side can then be represented as 2x - 5. Since the perimeter of the triangle is 23 cm, we can set up an equation:
x + x + (2x - 5) = 23
Now we can solve for x:
4x - 5 = 23
4x = 28
x = 7
Therefore, the length of the third side is 2(7) - 5 = 9 cm.
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Each of my daughters has as many brothers as sisters, but each of my sons has three times as many sisters as brothers. How many children do I have?
The family has 3 sons and 3 daughters, for a total of 6 children.
Explanation:
The question is a problem in basic algebra which can be solved using simple logical reasoning. We are given that each daughter in the family has as many brothers as sisters, and each son has three times as many sisters as brothers.
Let's start by saying that the number of daughters is D and the number of sons is S.
If each daughter has the same number of brothers as sisters, that means D = S. But, each son has three times as many sisters as brothers, which we can express as S = 3*(D - 1), because the number of sisters for each son is the number of daughters minus one (each son doesn't count himself as a sister).
By substituting D from the first equation into the second, we get S = 3 * (S - 1), which simplifies to S = 3, and thus D = 3 as well.
So, the family has 3 sons and 3 daughters, for a total of 6 children.
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Using the speaking outline, how many times should you practice? five or more three two one
According to the speaking outline, it is recommended to practice your speech at least five times or more.
According to the speaking outline, you should practice your speech "five or more" times. Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation. The more you practice, the better prepared you'll be to deliver a successful speech.
Therefore, it is recommended to practice your speech at least five times or more.
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According to the speaking outline, it is recommended to practice your speech at least five times or more.
According to the speaking outline, you should practice your speech "five or more" times.
Practicing your speech multiple times helps you become more familiar with the content, improve your delivery, and gain confidence in your presentation.
The more you practice, the better prepared you'll be to deliver a successful speech.
Therefore, it is recommended to practice your speech at least five times or more.
for such more question on times
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Find the simple interest on a loan of $3,500 at 7.8% interest for 9 months
BRAINLIESTTTTT
1. Write the equation of the line that passes through the points (3, 6) and (4, 10) using function notation.
f(x) = 4x − 6
f(x) = x + 4
y = x + 4
y = 4x − 6
Answer:
1. f(x) = 4x -6
2. see the attachment
Step-by-step explanation:
1. The only two answer choices using "function notation" are the first two, which are of the form ...
f(x) = <some expression involving x>
The only one of these that can describe both points is the first one:
f(x) = 4x -6
f(3) = 4·3 -6 = 6
f(4) = 4·4 -6 = 10
__
2. Slope is the ratio of rise to run. When it is zero, there is no rise for any amount of run: the line is horizontal. The appropriate choice is the graph that shows a horizontal line.
Given B = {a, l, g, e, b, r} and C = {m, y, t, h}, find B ∪ C
true or false circumference is the distance around the outside of a circle.
if b is between a and c then ab+bc=ac
What is the product (6r-1)(-8r-3)
Kristin is 20 miles behind a truck that is driving 50 miles per hour. How long will it take her to catch up to the truck? How far will she go in that time
It will take Kristin 24 minutes to catch up to the truck. She will travel a distance of 20 miles in that time.
Explanation:To calculate how long it will take for Kristin to catch up to the truck, we can use the equation: time = distance / speed. Since Kristin is 20 miles behind the truck, she will need to cover a distance of 20 miles to catch up to the truck. Assuming she drives at a constant speed, we can use her speed as the truck's speed since she needs to match it to catch up.
Time to catch up = 20 miles / 50 miles per hour = 0.4 hours = 24 minutes.
In that time, Kristin will travel the same distance as the truck. So, she will go 20 miles in 24 minutes.
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which fraction is less than 7/15
A: 5/9
B: 6/11
C: 1/2
D: 4/9
PLEASE HELP!!!
1. The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).
Determine the slope of each side of the triangle and use that information to determine if the triangle is a right triangle or not.
2.The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2).
Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram
If one candy bar weighs 3 ounces what is the weight of 11 candy bars
Final answer:
The weight of 11 candy bars is calculated by multiplying the weight of one candy bar, which is 3 ounces, by 11. The total weight for 11 candies is equal to 33 ounces.
Explanation:
If one candy bar weighs 3 ounces, the weight of 11 candy bars can be found by multiplying the weight of one candy bar by the number of candy bars. The calculation would be as follows:
Multiply the weight of one candy bar by the number of candy bars: 3 ounces × 11 = 33 ounces.
Therefore, the weight of 11 candy bars is equal to 33 ounces.
Rewrite the expression as a polynomial in standard form.
The expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) can be rewritten in standard form as -2x³ + 5x² - 16x
How did we get the value?To rewrite the expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) as a polynomial in standard form, we can combine like terms.
First, let's distribute the negative sign in front of the parentheses:
(2x² - x³ - 9x + 1) - x³ - 7x + 3x² - 1
Next, let's group the like terms together:
2x² + 3x² - x³ - x³ - 9x - 7x + 1 - 1
Now, let's combine the terms:
(2x² + 3x²) + (-x³ - x³) + (-9x - 7x) + (1 - 1)
5x² - 2x³ - 16x + 0
Finally, the expression (2x² - x³ - 9x + 1) - (x³ + 7x - 3x² + 1) can be rewritten in standard form as:
-2x³ + 5x² - 16x
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Could someone help with 14 I know it’s not a Consecutive interior but it could be A) alternate interior B) alternate exterior C) corresponding D) exterior
You are paid $82.50 for 7 1/2 hours of work. What is your rate of pay?