just show the right answer, i don’t need the work or explanation or anything

QUESTION 1

11

1. Assume that the matrix 2 1 represents a map h: RM R” with resoect to the standard bases.

31

State m and n.m=

n =

QUESTION 2

Find the rank and nullity of the linear map from question #1.

The rank is

The nullity is

-3

Find the image of the vector

under the linear map given by question #1,

BLANK1

Ans = BLANK

BLANK3

BLANK1 =

BLANK2 =

BLANK3 =

QUESTION 6

11

Solve the syster 2 1

31

(61):1-8)

BLANK1

BLANK4

The solution is

BLANK2 b + BLANKS Cb,CER

BLANK3

BLANK6

BLANK1 =

BLANK2 =

BLANK3 =

BLANK4 =

BLANK5 =

BLANK 6 =

Introduction:

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What is the matrix representing a map h with respect to the standard bases in question #1?

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This data provides information about a linear map h:RM->Rn represented by a matrix 2×1 with respect to the standard bases. The data also includes the rank and nullity of this map, the image of a vector under the linear map, and the solution of a system of equations.

Description:

In question #1, we are asked to assume a matrix 2×1 represents a linear map h:RM->Rn with respect to the standard bases. We are then asked to determine the values of m and n, for which m=n. In question #2, we are asked to find the rank and nullity of the linear map from question #1. We are then presented with a question asking us to find the image of a vector under the linear map given by question #1. Lastly, we are asked to solve a system of equations and provide the solution in terms of b, c, and Cb,CER.

Objectives:

1. To understand and apply matrix representation of linear maps.

2. To determine the rank and nullity of a linear map.

3. To solve a system of linear equations.

Learning Outcomes:

1. Students will be able to represent a linear map using a matrix.

2. Students will be able to calculate and interpret the rank and nullity of a linear map.

3. Students will be able to solve a system of linear equations using matrix methods.

Heading:

Linear Algebra

Solution 1:

m = 3, n = 2

Solution 2:

The rank is 2.

The nullity is 1.

The image of the vector under the linear map given by question #1 is not provided, hence cannot be answered.

The solution to the system is:

x = -8b + c

y = 4b + 3c

z = b

where b and c belong to real numbers.

Therefore,

BLANK1 = -8b + c

BLANK2 = 4b + 3c

BLANK3 = b

BLANK4 = b

BLANK5 = -8

BLANK6 = 4

Suggested Resources/Books:

– Linear Algebra by Gilbert Strang

– Introduction to Linear Algebra, Fifth Edition by Gilbert Strang

– Linear Algebra: A Modern Introduction 4th Edition by David Poole

Similar asked questions:

1. How do you find the rank and nullity of a linear map?

2. What is the difference between a matrix and a linear map?

3. How do you solve a system of linear equations?

4. What is the standard basis in linear algebra?

5. What is the significance of the determinant in linear algebra?

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