(29(29[ ]2230120030120030030000030000000000000000AaIAaI -==⇒-== 1c.Using the fact thatIandAcommutes, we have(t A aIAtatIatIAtatIatIAtatIeeeeeeee---===NoteatIateeI=(as shown in class)(1a)(29(29(29(29[ ]23230[0]2!3!t A aItteIt AaIAaIAaI-=+-+-+-+14243(1b)In (1b), we used (1b), i.e.,(29[ ](29[ ]300nAaIAaI-=⇒-=for3n≥.Combining(1a,b), we have(29(29(29(2922222!2AtatattteeIItAaIAaIeItAaIAaI=+-+-=+-+-1d.The solution of the initial value problem is(29(29220000200020120030030002000000AtatatteueutAaI uAaIuteutuu=+-+-=++rrrrrrrSubstituting[](0)0,0,1Touu==rrgives:20230302100attue