How does the number of solutions of a system depend on ranks of the coefficient matrix and the augmented matrix?
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Answer:
The number of solutions of a system is given by the number of different variables in the system, this number has to be the same as the number of independent equations. The coefficients and the augmented matrix of the system show these values in a matrix form. A system has a unique solution when the rank of both matrixes and the number o variables in the system are the same.
Step-by-step explanation:
For example, the following system has 2 different variables, x and y.
In order to find a unique solution to the system, the number of independent equations and variables in the system must be the same In the previous example, you have 2 independent equations and 2 variables, then the solution of the system is unique.
The rank of a matrix is the dimension of the vector generated by the columns, in other words, the rank is the number of independent columns of the matrix.
According to Rouché-Capelli Theorem, a system of equations is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. The inconsistency of the system is because you can't find a combination of the variables that will solve the system.
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Answer:
197/ 50 or in decimal 3.94
Answer
197/ 50 or in decimal 3.94
Step-by-step explanation:
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Answer:
math is hard :(
Step-by-step explanation:
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The random sampling method is used.
What is random sampling?
Random sampling is a statistical method of selecting a representative sample of individuals from a larger population in a way that ensures every member of the population has an equal chance of being chosen. In other words, each individual in the population has an equal probability of being selected for the sample, and the selection process is not biased towards any particular subgroup or characteristic of the population.
The sampling method used in this scenario is simple random sampling. This is because the survey is being given to a randomly selected group of students from the entire student body, where every student has an equal chance of being selected. The administration used a random number generator to select 100 numbers at random, which is a common method for achieving simple random sampling. This method is useful because it helps to eliminate bias in the selection process and ensures that the sample is representative of the entire population.
Hence, the random sampling method is used.
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Answers
The given triangle is a righttriangle.
Option E is the correct answer.
What is a triangle?
A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The sum of the angles must be 180.
So,
45 + 45 + 90 = 180
This is a condition for the right triangle.
Thus,
The given triangle is a righttriangle.
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D and E
the triangle is right as it has a right angle as one of the 3 angles
the triangle is isosceles as it has 2 equal sides , indicated by the score on the equal sides and 2 equal base angles of 45°
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There are 95 cards did Steve initially purchase to begin his collection.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Steve began a baseball card collection by purchasing some cards.
And, He increased the number of cards in the collection by a constant amount each week after that.
Now, In 3 weeks he collect 285 cards.
Hence, Number of cards to collect in initially is,
⇒ 285/3
⇒ 95
Thus, There are 95 cards did Steve initially purchase to begin his collection.
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Answer:95
Step-by-step explanation:
95x3=285
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-5 = -3/2 (6) + b
You use y = mx + b
Y is -5
M is the slope = -3/2
X is 6
B is the y intercept but that is not given