In Exercises
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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
- 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 Exercises30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2]=[x1x2x1+x2],S[y1y2]arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 4. defined by , where B is a fixed matrixarrow_forward
- In Exercises 30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2x3]=[x1+x2x32x1x2+x3],S[y1y2]=[4y12y2y1+y2]arrow_forwardIn Exercises 7-10, find the standard matrix for the linear transformation T. T(x,y)=(3x+2y,2yx)arrow_forwardIn Exercises30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2x3]=[x1+2x22x2x3],S[y1y2]=[y1y2y1+y2y1+y2]arrow_forward
- In Exercises 20-25, find the standard matrix of the given linear transformation from β2 to β2. 24. Reflection in the line y = xarrow_forwardProve part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix over. With as defined in the preceding paragraph,arrow_forwardIn Exercises 30-35, verify Theorem 3.32 by finding the matrix of ST (a) by direct substitution and (b) by matrix multiplication of [S] [T]. T[x1x2]=[x1+2x23x1+x2],S[y1y2]=[y1+3y2y1y2]arrow_forward
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