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yuradex [85]
3 years ago
5

Determine if the statement is true or false, and justify your answer. Suppose A is a matrix with n rows and m columns. If n <

m, then the columns of A span Rn.
Mathematics
1 answer:
Natali5045456 [20]3 years ago
6 0

Answer:

The question is incomplete as there are given options ;

Q:

Determine if the statement is true or false , and justify your answer . Suppose A is a matrix with n rows and m columns . If n < m, then the columns of A span R True, since there are more columns than rows. O False, since there are not enough columns to span R". True, since every column of A must be a nonzero column, False, since every column of A may be a zero column, True, since every column of A must be a non zero column, False, since every column of A may be a zero column

Step-by-step explanation:

Considering a matrix A with n-rows and m-columns,

given that n is less than m i.e the rows is less than the columns

then the columns of A span Rn? TRUE OR FALSE?

the matrix is of nxm as n is less than m, hence from linear transformation, T will span : Rm towards Rn

the concept of ranking of a matrix is applied here as ranking entails the  number of linearly independent rows or columns vectors in a matrix, in this case

the order is n x m where n is less than m, as such the rank of the matrix is n

So, Rank of MATRIX A is n

To prove if the rows vectors are linearly independent or not since n is the rank of the matrix

In this case, m columns vector will be considered with respect to n which is the rank and which is also less than m from the conditions, as such there exist a linearly independent relationship between them which R may be spanned since we know that from ranking, reduction to echelon form comes into play by trying to reduce every element of the column A to zero.

  • Trying to reduce to echelon form implies all the element of column A may or may not zero.

from the foregoing, the last option is the correct answer ; False, since every column of A may be a zero column

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Answer:

Second Option

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Step-by-step explanation:

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The result of that multiplication will be

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Therefore we have the expression

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By multiplying by the conjugate of the denominator we have

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8. There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random without replacement.
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Answer:

a. 720

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Step-by-step explanation:

a.

Three balls are selected at random without replacement.

First ball can be selected in 10 ways

Second ball can be selected in 9 ways

Third ball can be selected in 8 ways

Thus, there are 10×9×8 =720 different ways of selecting three balls.

b.

There are three cases that satisfy this condition

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Each probabilities are:

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  3. \frac{9}{10} *\frac{8}{9} *\frac{1}{8} =\frac{1}{10}

Thus, one of the balls selected is the number 5 is then \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10}

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