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
Answer:
25
Step-by-step explanation:
Formula
2xy + 1
Givens
x = 3
y = 4
Solve
2*(3)*(4) + 1
24 + 1
25
C - 17 > 33 is the answer
Difference = -
More than = >
2(2x − 1) > 6 or x + 3 ≤ −6
2(2x − 1) > 6
4x - 2 > 6
4x > 8
x > 2
or
x + 3 ≤ −6
x ≤ - 9
Solution: x ≤ - 9 or x > 2
(- ∞ , - 9] or (2 , + ∞)
Answer is the first one
(- ∞ , - 9] or (2 , + ∞)
