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
Hi there.
These two angles sum up to be 180 degrees, so they are supplementary angles. Now, since these angles sum up to 180 degrees (to form a straight line), we only have to subtract 133 from 180 to find angle 2's measurement.
180 - 133 = 47
Angle 2's measurement is 47 degrees.
Voila!
I hope this helps! Have a great day. :)
Carrie could have 3 vases filled with 100 marbles, and 4 vases filled with 10 marbles. Hope I helped!
Answer:
24.61%
Step-by-step explanation:
The distance covered in first week = 195 miles
The distance covered in the second week = 243 miles
We need to find the percentage increase in distance. It can be calculated as follows :
So, the increase in distance is equal to 24.61%.
