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:
5 times as large
Step-by-step explanation:
You can think of "10^5" as "green marbles" if you like. Then your question is ...
5 green marbles is how many times as large as 1 green marble.
Hopefully, the answer is all too clear: it is 5 times as large.
_____
In math terms, when you want to know how many times as large y is as x, the answer is found by dividing y by x:
y/x . . . . . tells you how many times as large as x is y.
Here, that looks like ...
Step-by-step explanation:
Length = L
Width = W
L=8 more than 2W
L = 8 * 2W
L = 16W
Perimeter = 96
perimeter is the lengths of all sides added together
so
2L + 2W = 96
we have
L = 16W
2L + 2W = 96
let's do substitution
put what L = into 2L + 2W = 96
so
2(16W) + 2W = 96
can you rearrange that to get w
put answer in comment
Answer:
15 inches
Step-by-step explanation:
Suppose length of original square is L inches.
Now, to form a new square the length increases by 2.5 inches
So, new length=L+2.5 inches
Given that, perimeter of new square =70 inches.
Formula:-
Perimeter=4*length of square
Therefore 70=4*(L+2.5)
70 =4 L+10
4 L=60
L=15 inches
