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:
Step-by-step explanation:
Given expression:
Replace 900 with 30² :
(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).
Simplify:
(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).
Answer:
4 parts
Step-by-step explanation:
If the total number of parts is 12 and you want to reduce the dish to two-thirds its current size, the number of parts that will be reduced is (1 - 2/3) = 1/3
To reduce 1/3 of the 12 parts, you need to multiply 12 by 1/3 to know how many parts is that:
12 * 1/3 = 12/3 = 4
You need to subtract 4 parts. If you have 4 ingredients, you can remove 1 part of each, so each ingredient now will have 2 parts.
Answer:
I can maybe!
OK, sorry it took me so long I wanted to make sure I gave you the best answer I could so I had to think a little. Anyway. If I had to pick one I would choose...
D. The value of g(x) is determined by the value of h times x.
I really hope this helps! I tried my best!
