............... Determine if the T is a linear transformation. T(x1, x2) = (5x, + x2, -4X1 + 7x2) O The function is a linear transformation. O The function is not a linear transformation. If so, identify the matrix A such that T(x) = Ax. (If the function is not a linear transformation, enter DNE into any cell.) A = If not, explain why not. O The function is a linear transformation. O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + c, b + d) + T(a, b) + T(c, d). O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + , b + d) = T(a, b) + T(c, d). O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) # aT(b, c). O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) = aT(b, c).

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 1EQ
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...............
Determine if the T is a linear transformation.
T(x1, x2) = (5x, + x2, -4X1 + 7x2)
O The function is a linear transformation.
O The function is not a linear transformation.
If so, identify the matrix A such that T(x) = Ax. (If the function is not a linear transformation, enter DNE into any cell.)
A =
If not, explain why not.
O The function is a linear transformation.
O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + c, b + d) + T(a, b) + T(c, d).
O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + , b + d) = T(a, b) + T(c, d).
O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) # aT(b, c).
O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) = aT(b, c).
Transcribed Image Text:............... Determine if the T is a linear transformation. T(x1, x2) = (5x, + x2, -4X1 + 7x2) O The function is a linear transformation. O The function is not a linear transformation. If so, identify the matrix A such that T(x) = Ax. (If the function is not a linear transformation, enter DNE into any cell.) A = If not, explain why not. O The function is a linear transformation. O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + c, b + d) + T(a, b) + T(c, d). O The function is not a linear transformation, since there exist numbers a, b, c, and d such that T(a + , b + d) = T(a, b) + T(c, d). O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) # aT(b, c). O The function is not a linear transformation, since there exist numbers a, b, and c such that T(a(b, c)) = aT(b, c).
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