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mixas84 [53]
3 years ago
8

If x = 2 and y =3. evaluate 3x - 4y

Mathematics
1 answer:
insens350 [35]3 years ago
6 0
The answer is -6 just plug in the values
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If the subspace of all solutions of Ax 0 has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A
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Question: If the subspace of all solutions of

Ax = 0

has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A.

Note: The rank of A can only be determined if the dimension of the matrix A is given, and the number of vectors is known. Here in this question, neither the dimension, nor the number of vectors is given.

Assume: The number of vectors is 3, and the dimension is 5 × 8.

Answer:

The rank of the matrix A is 5.

Step-by-step explanation:

In the standard basis of the linear transformation:

f : R^8 → R^5, x↦Ax

the matrix A is a representation.

and the dimension of kernel of A, written as dim(kerA) is 3.

By the rank-nullity theorem, rank of matrix A is equal to the subtraction of the dimension of the kernel of A from the dimension of R^8.

That is:

rank(A) = dim(R^8) - dim(kerA)

= 8 - 3

= 5

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3 years ago
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