Suppose that 22 inches of wire costs 66 cents.

Mathematics

1 answer:

GaryK [48]3 years ago

8 0

Answer:

51 cents for 17 inches of wire

Step-by-step explanation:

22 = 66

17 = x

22x = 66 * 17

22x = 1122

x = 51 cents

22 inches costs 66 cents

1 inch costs 3 cents (66 / 22 = 3 cents)

17 inches costs 51 cents (17 * 3 = 51 cents)

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Determine whether the set of vectors is a basis for ℛ3. Given the set of vectors , decide which of the following statements is t

schepotkina [342]

Answer:

(A) Set A is linearly independent and spans $R^3$ . Set is a basis for $R^3$ .

Step-by-Step Explanation

Definition (Linear Independence)

A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.

Definition (Span of a Set of Vectors)

The Span of a set of vectors is the set of all linear combinations of the vectors.

Definition (A Basis of a Subspace).

A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.

Given the set of vectors $A= \left(\begin{array}{[c][c][c][c]}1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1\\ 0 & 0 & 1 & 1\end{array} \right)$ , we are to decide which of the given statements is true:

In Matrix $A= \left(\begin{array}{[c][c][c][c]}(1) & 0 & 0 & 0\\ 0 & (1) & 0 & 1\\ 0 & 0 & (1) & 1\end{array} \right)$ , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column. $R^3$ has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans $R^3$ .