Determine if the given function is a linear transformation. 0 0 1 T: M3,3 → M3,3) T(A) = 0 10 A

Determine which of the following functions are linear transformations. For each function, either prove that it is a linear transformation of explain why it is not. (a) S: R² R² given by (b) T: P₂ → P₁ given by I s([*]) = [2+³+1] T(co+c₁x + c₂²) = −c₁ + ₂x. where co, C1, C₂ are constants. (c) F: M2,2 M2,2 given by F(A) = A-AT.

Which of the following transformations are linear? Check all that apply. Note you only have 5 attempts. (E]). [4x - 5y + 2z 9y - 7z = -10x - 3y -2x 5x 8x [6x] A. T B. T C. T OD. T ([]) ¹ ([₁]) = x E. T ([]) F. T = = (1) (1) = = [7x + -X 7 30 10 [y²] N X '5

please solve part d

Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. 0 A. T(A) = SAS-1 from R2x2 to R2x2, where S = 0 4 3 -7 c. T(A) = ASA-¹ from R2x2 to R²x2, where S = B. T(A) = A from R2x3 to R2x3 OD. T(A) = trace(A) from R6x6 to R DE. T(A) = A + 13 from R³x3 to R³x3 7 5 F. T(A) = A 6 5 $]-[1 4 8 -3 -4 5 A from R2x2 to R²x2 9

3. Explain why whenever A is a Ax = 0 always has linear transformation, solution

Helena, Mont. has an average July temperature of 67.8 degrees Fahrenheit. What is this average if temp is expressed in Celsius? (Round to two decimal places.) [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]

Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. □A. T(f(t)) = (f(t))³ + 6(f(t))² + 5f (t) from C to C B. T(x0, X₁, X2, ...) = (1, X0, X₁, X₂, ...) from the space of infinite sequences into itself C. T(f(t)) = f(9) from P7 to R D. T(f(t)) = f(-t) from P5 to P5 □E. T(f(t)) = f'(t) + 6f (t) from C* to C* = [₁₁ □ F. T(f(t)) = f(t)dt from P3 to R

Please answer correctly this time

Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(A) = det(A) from R5x5 to R B. T(A) = trace(A) from R6x6 to R 1 C. T(A) = D. T(A) = AT from R3x5 to R5x3 E. T(A) = A7 from R 4x4 to R4x4 F. T(A) = 6A from R4x5 4x5 to R4 2₁ A from R2x3 to R2x3