Linear Transformation

Consider a 3 dimension system. Linear transformation in 3D along with its matrix form is given by

Note: If Y=AX and Z=BY,then Z=(BA) X=Composite Linear Transformation.


Linear Transformation

Linear Transformation Problems

  1. Show that the transformation y_1=x_1+2x_2+5x_3 ; y_2=2x_1+4x_2+11x_3 ; y_3= -2x_2+2x_3 is regular. Write down the inverse transformation
  2. Show that the transformation y_1=2x-2y-z ; y_2= – 4x+5y+3z ; y_3=x-y-z is regular and find out the Inverse transformation.
  3. Show that the transformation y_1=2x+y+z ; y_2=x+y+2z; y_3=x-2z is regular. Write down the inverse transformation
  4. Verify the transformation y_1=19 x_1-9x_2+2x_3; y_2=-4x_1+2x_2-x_3;y_3=-2x_1+x_2 is regular or not and find the Inverse transformation if possible


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