Suppose s is a six-dimensional subspace of nine-dimensional space r 9 .

(a) what are the possible dimensions of subspaces orthogonal to s?

(b) what are the possible dimensions of the orthogonal complement s j_ of s?

( c) what is the smallest possible size of a matrix a that has row space s?

(d) what is the smallest possible size of a matrix b that has nullspace s j_ ?

hi,

3. 12.15, you are correct.

4.2.01, your first digit is correct,

hope this !

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!