please do 4.2.1 ; 4.2.2; 4.2.3 Question 4[2Let Aj = l: A2 =M2. Answer the following questions:4.2)Az =and A4be matrices in4.2.1) For which values of A will S =set? Show all calculations.{A1, A2, A3, A4} form a linearly independent4.2.2) Let B = " a be a matrix in Mm. Set up a linear system of equations thatneed to be satisfied such that B is spanned by the vectors in S.4.2.3) Use the system in question 4.2.2 to find out if there are values of A for whichthe set S = {A1, A2, A3, A4} will be a basis for My. If there are such values, findthem all.

Name: please do 4.2.1 ; 4.2.2; 4.2.3 Question 4[2Let Aj = l: A2 =M2. Answer
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Description: please do 4.2.1 ; 4.2.2; 4.2.3 Question 4[2Let Aj = l: A2 =M2. Answer the following questions:4.2)Az =and A4be matrices in4.2.1) For which values of A will S =set? Show all calculations.{A1, A2, A3, A4} form a linearly independent4.2.2) Let B = " a b

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Question 4 42) Let A-3 이. A-3. M2. Answer the following questions: Az = and A = 0 ôl be matrices in 4.2.1) For which values of A will S = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. 4.2.2) Let B = " a be a matrix in Mn. Set up a linear system of equations that need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S = {Aj, A2, A3, Ã4} will be a basis for M. If there are such values, find them all. 10

Question 4 42) Let A-3 이. A-3. M2. Answer the following questions: Az = and A = 0 ôl be matrices in 4.2.1) For which values of A will S = {A1, A2, A3, A4} form a linearly independent set? Show all calculations. 4.2.2) Let B = " a be a matrix in Mn. Set up a linear system of equations that need to be satisfied such that B is spanned by the vectors in S. 4.2.3) Use the system in question 4.2.2 to find out if there are values of A for which the set S = {Aj, A2, A3, Ã4} will be a basis for M. If there are such values, find them all. 10

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.4: Determinants

Problem 52PS

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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