ifiotdedepleamning di datsmachine vrartificialintelligencedx Given a matrix M : M=2621r4322 (a) Calculate the determinant of M in terms of r (calculation process is required). [4pts] (b) For what value(s) of r does M1 not exist? Why doesn't M1 exist in this case? What does it mean in terms of rank and singularity for these values of r?[3pts] (c) Will all values of r found in part (b) allow for a column (or row) to be expressed as a linear combination of the other columns (or rows)? If yes, provide - either the linear equation of the third column C3 as a linear combination of the first column C1 and second column C2 - or the linear equation of the second row R2 as a linear combination of the first row R1 and third row R3. If no, explain why. [3pts] (d) Write down M1 for r=0 (calculation process is NOT required). [2pts] (e) Find the mathematical equation that describes the relationship between the determinant of M and the determinant of M1. [3pts] NOTE: It may be helpful to find the determinant of M and M1 for r=0