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linear algebra 1 0 0 0 1 1 0 0 1. Let A be the 4 x 4 matrix: A= 1 1 1 0 1 1 1 1 (a) Find A-1 by hand. (b) Let T be defined by T(T) = Aē. Use your answer to (a) to find all vectors T E R4 such that: T(T) = 2 4 -9 0 (c) Which of the following statements are true? (Select all that apply) A. The columns of A form...

• ### Please give answer with the details. Thanks a lot! Let T: V-W be a linear transformation between vector spaces V and W...

Please give answer with the details. Thanks a lot! Let T: V-W be a linear transformation between vector spaces V and W (1) Prove that if T is injective (one-to-one) and {vi,.. ., vm) is a linearly independent subset of V the n {T(6),…,T(ền)} is a linearly independent subset of W (2) Prove that if the image of any linearly independent subset of V is linearly independent then Tis injective. (3) Suppose that {b1,... bkbk+1,. . . ,b,) is a...

• ### Let T: V + W be a linear transformation. Assume that T is one-to-one. Prove that...

Let T: V + W be a linear transformation. Assume that T is one-to-one. Prove that if {V1, V2, V3} C V is a linearly independent subset of V, then {T(01), T(v2), T(13)} C W is a linearly independent subset of W.

• ### (1 point) Let f:R → R'be the linear transformation defined by T 4 -5 51 f(T)...

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a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...

• ### is onto is o Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R Give some examples of the echelon forms. The leading entries, denoted , may have any n...

is onto is o Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R Give some examples of the echelon forms. The leading entries, denoted , may have any nonzero value; the starred entries, denoted , may have any value (including zero). Select all that apply C. 0 0 0 0 B. A. E. 0 G. 0 is onto is o Describe the possible echelon forms of the standard matrix for a linear...

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Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...