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:
x=
−4
/3
y+5
Step-by-step explanation:
The answer is 137° because supplementary means the 2 angles must equal 180°
False if y=f(x) then x= inverse of f(x) or f^-1(x)
The triangle drawn in the question shows a small single line drawn across two sides of the triangle.
This means that those two sides are equal in length.
Hence, the triangle is an isosceles triangle.
In isosceles triangles, the angles opposite to the equal sides are also equal.
Hence, we know that the two angles other than x is 56°.
The sum of the interior angles of a triangle is 180°
x + 56 + 56 = 180
x = 180 - 56 - 56
x = 180 - 112
x = 68°
Hence, the answer is A.
