Problem $2\mathrm{.}3$ The elements of a$48$ matrix is given in the following table. Let us denote the

matrix by A$.$ Perform matrix calculations from this matrix $($A$)$ using PROC IML in SAS or

matrix algebra in R$.$

A col$1$ col$2$ col$3$ col$4$ col$5$ col$6$ col$7$ col$8$

row$1-0\mathrm{.}67581\mathrm{.}1878950\mathrm{.}05993-1\mathrm{.}410420\mathrm{.}2493590\mathrm{.}684817-1\mathrm{.}482780\mathrm{.}905952$

row$2-0\mathrm{.}304181\mathrm{.}308264-1\mathrm{.}105040\mathrm{.}266421\mathrm{.}651046-0\mathrm{.}564421\mathrm{.}9102251\mathrm{.}523252$

row$3-0\mathrm{.}719681\mathrm{.}6374171\mathrm{.}079418-0\mathrm{.}094620\mathrm{.}6990590\mathrm{.}434304-0\mathrm{.}466591\mathrm{.}606218$

row$4-1\mathrm{.}18086-0\mathrm{.}69885-2\mathrm{.}158081\mathrm{.}189356-0\mathrm{.}557770\mathrm{.}0084910\mathrm{.}7593541\mathrm{.}285645$

$(1)$ Calculate A $+0\mathrm{.}5$A$,$ which is equivalent to $(1+0\mathrm{.}5)$A $=1\mathrm{.}5$A

$(2)$ FindT

A

$(3)$ CalculateT

B $=$ AA

$(4)$ Calculate the determinant ofT

B $=$ AA

$(5)$ Calculate$1$ T $1$

B $($AA $)$

$=$

$(6)$ Calculate ATA

$(7)$ Calculate the eigenvalues and eigenvectors of matrixT

B $=$ AAProblem $2\mathrm{.}3$ The elements of a$48$ matrix is given in the following table. Let us denote the

matrix by A$.$ Perform matrix calculations from this matrix $($A$)$ using PROC IML in SAS or

matrix algebra in R$.$

A col$1$ col$2$ col$3$ col$4$ col$5$ col$6$ col$7$ col$8$

row$1-0\mathrm{.}67581\mathrm{.}1878950\mathrm{.}05993-1\mathrm{.}410420\mathrm{.}2493590\mathrm{.}684817-1\mathrm{.}482780\mathrm{.}905952$

row$2-0\mathrm{.}304181\mathrm{.}308264-1\mathrm{.}105040\mathrm{.}266421\mathrm{.}651046-0\mathrm{.}564421\mathrm{.}9102251\mathrm{.}523252$

row$3-0\mathrm{.}719681\mathrm{.}6374171\mathrm{.}079418-0\mathrm{.}094620\mathrm{.}6990590\mathrm{.}434304-0\mathrm{.}466591\mathrm{.}606218$

row$4-1\mathrm{.}18086-0\mathrm{.}69885-2\mathrm{.}158081\mathrm{.}189356-0\mathrm{.}557770\mathrm{.}0084910\mathrm{.}7593541\mathrm{.}285645$

$(1)$ Calculate A $+0\mathrm{.}5$A$,$ which is equivalent to $(1+0\mathrm{.}5)$A $=1\mathrm{.}5$A

$(2)$ FindT

A

$(3)$ CalculateT

B $=$ AA

$(4)$ Calculate the determinant ofT

B $=$ AA

$(5)$ Calculate$1$ T $1$

B $($AA $)$

$=$

$(6)$ Calculate ATA

$(7)$ Calculate the eigenvalues and eigenvectors of matrixT

B $=$ AA