In Exercise
Give the formula for a linear transformation
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.arrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 24. Reflection in the line y = xarrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 25. Reflection in the linearrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB, where B is a fixed nn matrixarrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from2to 2. Projection onto the line y=2xarrow_forwardIn Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[xy+z2x+y3z]arrow_forward
- In Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 23. Projection onto the linearrow_forwardLet T be a linear transformation T such that T(v)=kv for v in Rn. Find the standard matrix for T.arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 4. defined by , where B is a fixed matrixarrow_forward
- In Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. T[xyz]=[x+zy+zx+y]arrow_forwardIn Exercises 11-14, find the standard matrix of the linear transformation in the given exercise. 11.arrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 21. Clockwise rotation through 30° about the originarrow_forward
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