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Example of Kernel and Range of Linear Transformation

MathDoctorBob 292,485 14 years ago
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Linear Algebra: Find bases for the kernel and range for the linear transformation T:R^3 to R^2 defined by T(x1, x2, x3) = (x1+x2, -2x1+x2-x3). We solve by finding the corresponding 2 x 3 matrix A, and find its null space and column span. We check our work using the Rank Equation. Note: This linear transformation is onto, but not one-one.

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