5. Let V and W and let T and S be linear transformation from ✓ V ^ that if T is invertible, then there are real numbers C be M-dimensional IR-vector spaces W. Show sit. T+cs is not } at most h in vertible.

Q: 27. Let S be the set of all vectors both of y in R' such that x + y -z = 0 and 2x – 3y + 2z = 0.…

A:

Q: For a pair of vectors u and v in R^2 are shown below, shade in the region containing all linear…

A: We are given the pair of vectors u→ and v→ as shown in the figure. Now, we need to shade the region…

Q: 6. List 3 non-zero vectors in R° that are orthogonal. (You must verify that they are orthogonal.)

A: See the detailed solution below.

Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

A: We will solve the following

Q: Find the projection of u = onto v = . projuv =

A: We can find the projection in two form one is in scalar form and other is vector form. here i give…

Q: 8. Let 1 2 +--+- () -- () ---(3) (:). at = and = 3 4 7 b3 (a) Find conditions on b₁,b2, b3 such that…

A:

Q: Find the domain of the vector functions, ?(?)�(�), listed below. using interval notation. ) ?(?)=⟨…

A: To find the domain of the vector function r(t)=⟨t−3,t2−4​1​,t1/3⟩, we need to consider the values of…

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

A:

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

A:

Q: 5. Prove that any finite set of vectors that contains the zero-vector must be linearly dependent.…

A: