Answer:
x = 1, y = 1
Step-by-step explanation:
Use system of equations to solve for x and y by using substitution
Basically, we need to find the lowest common multiple of 10 and 15.
that multiply would be 30. That means that the bells will ring together in 30 minutes.
So 30 minutes from 6 p.m. is 6:30 p.m. <==
Answer:
Sample Response: Start at the origin. The x-coordinate is −2½ , so move left 2½ units. −2½ is halfway between −3 and −2. The y-coordinate is −4, so move down 4 units. Plot the point.
Step-by-step explanation:
Answer:
The answer is cosx cot²x ⇒ the first answer
Step-by-step explanation:
∵ cot²x = cos²x/sin²x
∵ secx = 1/cosx
∴ cot²x secx - cosx = (cos²x/sin²x)(1/cosx) - cosx
= (cosx/sin²x) - cosx
Take cosx as a common factor
∴ cosx[(1/sin²x) - 1] ⇒ use L.C.M
∴ cosx[1-sin²x/sin²x]
∵ 1 - sin²x = cos²x
∴ cosx(cos²x/sin²x) = cosx cot²x
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
