Question

1 : H= (hij) 4×3, sendo hij
se j > i ; i - j / j 
Se j < i ; i - j / i
Se j = i ; j/ i ?


2 : B = (bij) 2×5 tal que bij = ( 3 i ) ao quadrado - ( 2 i ) ao quadrado ?

3: C = (cij ) 4×2 tal que cij = 4 i / j ao quadrado?

Answer 1

1) a11 = 1 / 1 = 1
a12 = 1 - 2 / 2 = 0
a13 = 1 - 3 / 3 = 0
a21 = 2 - 1 / 2 = 1,5
a22 = 2 / 2 = 1
a23 = 2 - 3 / 3 = 1
a31 = 3 - 1 / 3 = $\frac{8}{3}$
a32 = 3 - 2 / 3 = $\frac{7}{3}$
a33 = 3 / 3 = 1 
a41 = 4 - 1 / 4 = 3,75
a42 = 4 - 2 / 4 = 3,5
a43 = 4 - 3 / 4 = 3,25

H = $\left[\begin{array}{cccc}1&0&0\\1,5&1&1\\ \frac{8}{3} & \frac{7}{3} &1\\3,75&3,5&3,25\end{array}\right]$

2) a11 = (3*1)²-(2*1)² = 5
a12 = (3*1)²-(2*2)² = -7
a13 = (3*1)²-(2*3)² = -27
a14 = (3*1)²-(2*4)² = -55
a15 = (3*1)²-(2*5)² = -91
a21 = (3*2)²-(2*1)² = 32
a22 = (3*2)²-(2*2)² = 20
a23 = (3*2)²-(2*3)² = 0
a24 = (3*2)²-(2*4)² = -28
a25 = (3*2)²-(2*5)² = -64

B = $\left[\begin{array}{ccccc}5&-7&-27&-55&-91\\32&20&0&-28&-64\end{array}\right]$


3) a11 = 4*1/1² = 4
a12 = 4*1/2² = 1
a21 = 4*2/1² = 8
a22 = 4*2/2² = 2
a31 = 4*3/1² = 12
a32 = 4*3/2² = 3
a41 = 4*4/1² = 16
a42 = 4*4/2² = 4

C = $\left[\begin{array}{cc}4&1\\8&2\\12&3\\16&4\end{array}\right]$