A=⎝⎛3−11021⎠⎞,B=⎝⎛1405−12⎠⎞,C=⎝⎛213041125⎠⎞,D=(−130214),E=(−141123)
−4C2=−4⎝⎛213041125⎠⎞⋅⎝⎛213041125⎠⎞==−4⎝⎛4+0+32+4+66+1+150+0+10+16+20+4+52+0+51+8+103+2+25⎠⎞==−4⎝⎛71222118971930⎠⎞==⎝⎛−28−48−88−4−72−36−28−76−120⎠⎞
2.
(E−D)T==((−141123)−(−130214))T==((011−11−1))T==⎝⎛0111−1−1⎠⎞
3.
A(BC)
B:3×2,C:3×3
The product BC does not exist.
4.
(BTB)C
BT=(154−102),B=⎝⎛1405−12⎠⎞BT⋅B=(154−102)⋅⎝⎛1405−12⎠⎞==(1+16+05−4+05−4+025+1+4)=(171130)
BT⋅B:2×2,C:3×3
The product (BTB)C does not exist.
5.
3B−AB3B=3⎝⎛1405−12⎠⎞=⎝⎛312015−36⎠⎞
A:3×2,B:3×2
The product AB does not exist.
Then 3B-AB does not exist.
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