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:
9=0.6q where q is the number of questions on the exam.
Step-by-step explanation:
Let's put it this way.
It's a ratio of 6:72 and we need to change it in a way to find number of rooms cleaned in 9 days.
Divide 6 & 72 both by 2
Ratio is now 3:36
Multiply 3 & 36 both by 3
Ratio is now 9:108
The number of rooms in which Robin can clean in 9 days is 108 rooms.
Answer:
in
Step-by-step explanation:
Let x be the side of square.
Length of box=8-2x
Width of box=15-2x
Height of box=x
Volume of box=
Substitute the values then we get
Volume of box=V(x)=
Differentiate w.r.t x
Again differentiate w.r.t x
Substitute x=6
Substitute x=5/3
Hence, the volume is maximum at x=
Therefore, the side of the square ,
in cutout that gives the box the largest possible volume.
A=4-3b
subtract 4 from both sides
a-4=-3b
divide by -3 for both sides
(a-4)/-3 = b
