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

  

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 =

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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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