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amid [387]
3 years ago
12

If the null space of A4×5 is exactly a two-dimensional plane, answer the following:

Mathematics
1 answer:
Hatshy [7]3 years ago
8 0

Answer:

I.

A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4

Null space is exactly two dimensional plane

dim null (A) = 2

II.

Rank A = dim U - dim Null A = 5 - 2 = 3

III.

Number of linearly Independent columns of A is the rank of A = 3

IV.

Yes, The system Ax = b has no solution sometimes as range of A \neq V

V.

Yes,Sometimes Ax = b has a unique solution

VI.

Yes, sometimes Ax = b has infinitely many solutions

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3 years ago
Please help I really need it for a grade boost.
ArbitrLikvidat [17]

Answer:

I hope This will Help u.. Plz mark me as Brilliant please

Step-by-step explanation:

Before you get started, take this readiness quiz.

Simplify: 

If you missed this problem, review (Figure).

Solve Equations with Constants on Both Sides

In all the equations we have solved so far, all the variable terms were on only one side of the equation with the constants on the other side. This does not happen all the time—so now we will learn to solve equations in which the variable terms, or constant terms, or both are on both sides of the equation.

Our strategy will involve choosing one side of the equation to be the “variable side”, and the other side of the equation to be the “constant side.” Then, we will use the Subtraction and Addition Properties of Equality to get all the variable terms together on one side of the equation and the constant terms together on the other side.

By doing this, we will transform the equation that began with variables and constants on both sides into the form  We already know how to solve equations of this form by using the Division or Multiplication Properties of Equality.

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Solution

In this equation, the variable is found only on the left side. It makes sense to call the left side the “variable” side. Therefore, the right side will be the “constant” side. We will write the labels above the equation to help us remember what goes where.



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Use the Subtraction Property of Equality.Simplify.Now all the variables are on the left and the constant on the right.

The equation looks like those you learned to solve earlier.Use the Division Property of Equality.Simplify.Check:Let .

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Solve: 



Solve: 

Solution

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4 0
2 years ago
Read 2 more answers
A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?
Murljashka [212]

Answer:

6

Step-by-step explanation:

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5 0
3 years ago
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What is the area of the rectangle below?
egoroff_w [7]

Answer:

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Step-by-step explanation:

8 0
2 years ago
An airplane travels 6903 kilometers against the wind in 9 hours and 8613 kilometers with the wind in the same amount of time. Wh
Rzqust [24]

Answer:

The rate of the plane is 862 miles per hour

Step-by-step explanation:

An airplane travels 6903 kilometers against the wind in 9 hours.

Speed = distance / time

Speed of the airplane while travelling against the wind is

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The airplane travelled 8613 kilometers with the wind in the same amount of time. This means that the speed while travelling with the wind will be

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Let x = speed of the airplane

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Subtracting equation 2 from equation 1,

-y - y = 767 - 957

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y = -190/-2

y = 95 miles per hour

x = 957 - y

x = 957 - 95

x = 862 miles per hour

4 0
3 years ago
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