Ms. Sze is grading math tests. A student’s work on a problem is given below

Mathematics

1 answer:

trapecia [35]3 years ago

4 0

Answer:

No the student is not correct because the answer is 0.4761. All the student did was wrong was the adding up the zeros.

Step-by-step explanation:

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For this exercise assume that all matrices are ntimesn. Each part of this exercise is an implication of the form "If "statement

inna [77]

Answer:

C. True; by the Invertible Matrix Theorem if the equation Ax=0 has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the n x n identity matrix.

Step-by-step explanation:

The Invertible matrix Theorem is a Theorem which gives a list of equivalent conditions for an n X n matrix to have an inverse. For the sake of this question, we would look at only the conditions needed to answer the question.

There is an n×n matrix C such that CA= $I_n$ .
There is an n×n matrix D such that AD= $I_n$ .
The equation Ax=0 has only the trivial solution x=0.
A is row-equivalent to the n×n identity matrix $I_n$ .
For each column vector b in $R^n$ , the equation Ax=b has a unique solution.
The columns of A span $R^n$ .

Therefore the statement:

If there is an n X n matrix D such that AD=I, then there is also an n X n matrix C such that CA = I is true by the conditions for invertibility of matrix:

The equation Ax=0 has only the trivial solution x=0.

A is row-equivalent to the n×n identity matrix $I_n$ .

The correct option is C.

5 0

4 years ago

What is the system is equations 5x+4y=8 2x-3y=17

Tomtit [17]

Answer:

(4, -3)

Step-by-step explanation:

The system of equations can be described a number of ways. One possible description is "a consistent pair of linear equations in two variables."

Perhaps you want to know the solution to this system of equations. I find it easiest to graph them. The attached graph shows the solution to be ...

(x, y) = (4, -3)

You can also use "elimination" to simplify the system to a single equation in a single variable. Adding 4 times the second equation to 3 times the first will do that.

3(5x +4y) +4(2x -3y) = 3(8) +4(17)

23x = 92 . . . . . simplify

x = 4 . . . . . . . . divide by 23

Substituting this value into the first equation, we have ...

5(4) +4y = 8

5 +y = 2 . . . . . . divide by 4

y = -3 . . . . . . . . subtract 5

The solution is (x, y) = (4, -3).