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:
To do this question, we must first convert Pi to a decimal form, as shown below:
Pi = 3.14
So then our equation becomes:
3.14 x 36 - 16
We still need to remember PEMDAS.
Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
So according to PEMDAS, we need to do 3.14 x 36, which equals 113.04
Now we have to do:
113.04 - 16 = 97.04
Our answer is 97.04
<u><em>Hope this helps - genius423</em></u>
Answer:
B. Parallel
Step-by-step explanation:
Equation 1 simplified: y = 3x+7
Equation 2 simplified: y = -x/3-3
The slopes are completely different, ruling out the possibility of the lines being parallel.
But we also see the slopes of the equations are opposite and negative to each other. Making the lines perpendicular.
Answer:
If it's of which decimal than the answer will be 0.09
