Consider a matrix A with m rows. Which condition below will ensure that every vector in Rm is in the span of the columns of A? The linear transformation with standard matrix A is injective. A has no zero row. Every row of A is a pivot row. Every column of A has a pivot.

Let T be the linear transformation defined by T(1, 2, 3, 4, 5) = −9x1 + 7x2 + 4x3 + 6x4 + 8x5. Its associated matrix A is a matrix.

show that T is a linear transformation by finding a matrix that implements the mapping. Note that X₁, X₂, ... are not vectors but are entries in vector. 17. T(X1, X2, X3, X4) = (0, X₁ + X2, X2 + x3, x3 + x4) 19. T(X1, X2, X3) = (x₁ - 5x2 + 4x3, x2 - 6x3) 21. Let T: R² → R2 be a linear transformation such that T(x₁, x₂) = (x₁+x2, 4x₁ + 5x₂). Find x such that T(x) (3,8). =

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, ... are not vectors but are entries in vectors. T(X1.X2.X3.X4) = (X1 + 4×2. 0, 8x2 + X4. X2 - X4) A = (Type an integer or decimal for each matrix element.)

Assume that T is a linear transformation. Find the standard matrix of T. ← T: R² →R² first reflects points through the horizontal x₁-axis and then reflects points through the vertical x₂-axis. 10 01 (Type an integer or simplified fraction for each matrix element.) A = -wrung

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, ... are not vectors but are entries in vectors. T(x1,X2,X3,X4) = (×1 + 8X2, 0, 6×2 + X4, X2 – X4) A = |(Type an integer or decimal for each matrix element.)

If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, ... are not vectors but are entries in vectors. T(x1 X2 X3) = (*1 -2x2 +5x3, X2 - 9x3) A= (Type an integer or decimal for each matrix element.)

Suppose A is a 3 × 5 matrix, and B is a 5 x 3 matrix. Assuming that A, B act on vectors in IR", identify the domain and codomain of each of the following transformations. A: R →R BA: R R B: R R AB: R R Explain why AB + BA. Your explanation must be based on interpreting AB, BA as transformations. (This question will be graded after the due date) Edit Insert▾ Formats ▾ B I U @ ED X₂ x² A▾ ΣΕ Σ ΡΗ

Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, X2, ... are not vectors but are entries in vectors. T(X1,X2.X3) = (X1 - 8x2 + 7x3, X2 - 3x3) A = (Type an integer or decimal for each matrix element.)