For Problems 14-15, determine all the values of constant k for which the given set of vectors in linearly independent in ℝ 4 . { ( 1 , 0 , 1 , − 1 ) , ( 1 , k , 1 , 1 ) , ( 2 , 1 , k , 1 ) , ( − 1 , 1 , 1 , k ) } .
For Problems 14-15, determine all the values of constant k for which the given set of vectors in linearly independent in ℝ 4 . { ( 1 , 0 , 1 , − 1 ) , ( 1 , k , 1 , 1 ) , ( 2 , 1 , k , 1 ) , ( − 1 , 1 , 1 , k ) } .
Solution Summary: The author explains that the given vectors are linearly independent in R4.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
How would I find the basis and range rank for this linear algebra question?
X=
2
1
2
1
3
2
2
1
4
3
2
1
where the rows represent breakfast, lunch, and dinner, and the columns represent the number of exchanges for each of the four food groups at each meal;
Y=
5
0
7
0
10
1
0
15
2
10
12
8
where the rows represent the four food groups, and the columns represent the amount of fat, carbohydrates, and protein per exchange of each food group; and
Z=
8
4
5
where the rows represent fat, carbohydrates, and protein, and the column represents calories per exchange.
(a) Find the product matrix XY. What do the entries of this matrix represent?
(b) Find the product matrix YZ. What do the entries represent?
(c) Find the products 1XY2Z and X1YZ2 and verify that they are equal. What do the entries represent
For matrix (4 6 3 5) if f(X) =X squared -5 , calculate f (A)
Chapter 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
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