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:
3x-2y
Step-by-step explanation:
log10^(3x-2y)
We know the base is base 10 since it is not written
log10 10^(3x-2y)
The log10 10 cancels
3x-2y
Answer:
17 floors
Step-by-step explanation:
1 floor every 4 seconds.
90/4 = 22.5
40 - 22.5 = 17.5
17.5 is 17ish floors, and is the only answer that is close to 17 floors.
Let's define each choice to differentiate which is the answer
A. Equivalent - equivalent equations may not look exactly the same on face value. But they are equivalent because they have the same exact solution.
B. Expressions - expression is a general term for equations that are formed from word problems
C. Equal - equal equations are the exact duplicate of each other
D. Similar - this term is only used on geometric shapes to tell that the two shapes have a fixed ratio of their similar sides or angles
E. Radical - radical equations are those involving fractions
Therefore, from their descriptions, the answer is A.
