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
We can add or subtract integer. We can also subtract like terms.
Answer:
12
Step-by-step explanation:
you first make an equation of 5/6x = 10, then divide 5/6 on both sides to get x = 12
End behavior: f. As x -> 2, f(x) -> ∞; As x -> ∞, f(x) -> -∞
x-intercept: a. (3, 0)
Range: p. (-∞, ∞)
The range is the set of all possible y-values
Asymptote: x = 2
Transformation: l. right 2
with respect to the next parent function:
Domain: g. x > 2
The domain is the set of all possible x-values
Answer:
5 yr and 39 yr
Step-by-step explanation:
Let x = the age of the younger
then 7x + 4 = the age of the older
Now x + 7x + 4 = 44
8x + 4 = 44
8x = 40
x = 5
7x + 4 = 7(5) + 4 = 35 + 4 = 39
Check: 5 + 39 = 44
