Đại số tuyến tính Ví dụ

$899^{9} [\begin{array}{c} 8 & 69 & 9 & 61 \\ 4 & 5 & 5 & 5 \\ 4 & 5 & 87 & 7 \end{array}]$

Bước 1

Nâng $899$ lên lũy thừa $9$ .

$383563458231675000000000000 [\begin{array}{c} 8 & 69 & 9 & 61 \\ 4 & 5 & 5 & 5 \\ 4 & 5 & 87 & 7 \end{array}]$

Bước 2

Nhân $383563458231675000000000000$ với mỗi phần tử của ma trận.

$[\begin{array}{c} 383563458231675000000000000 \cdot 8 & 383563458231675000000000000 \cdot 69 & 383563458231675000000000000 \cdot 9 & 383563458231675000000000000 \cdot 61 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3

Rút gọn từng phần tử trong ma trận.

Nhấp để xem thêm các bước...

Bước 3.1

Nhân $383563458231675000000000000$ với $8$ .

$[\begin{array}{c} 3068507665853400000000000000 & 383563458231675000000000000 \cdot 69 & 383563458231675000000000000 \cdot 9 & 383563458231675000000000000 \cdot 61 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.2

Nhân $383563458231675000000000000$ với $69$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 383563458231675000000000000 \cdot 9 & 383563458231675000000000000 \cdot 61 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.3

Nhân $383563458231675000000000000$ với $9$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 383563458231675000000000000 \cdot 61 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.4

Nhân $383563458231675000000000000$ với $61$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.5

Nhân $383563458231675000000000000$ với $4$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.6

Nhân $383563458231675000000000000$ với $5$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.7

Nhân $383563458231675000000000000$ với $5$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 383563458231675000000000000 \cdot 5 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.8

Nhân $383563458231675000000000000$ với $5$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 \\ 383563458231675000000000000 \cdot 4 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.9

Nhân $383563458231675000000000000$ với $4$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 \\ 1534253832926700000000000000 & 383563458231675000000000000 \cdot 5 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.10

Nhân $383563458231675000000000000$ với $5$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 383563458231675000000000000 \cdot 87 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.11

Nhân $383563458231675000000000000$ với $87$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 33370020866155725000000000000 & 383563458231675000000000000 \cdot 7 \end{array}]$

Bước 3.12

Nhân $383563458231675000000000000$ với $7$ .

$[\begin{array}{c} 3068507665853400000000000000 & 26465878617985575000000000000 & 3452071124085075000000000000 & 23397370952132175000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 & 1917817291158375000000000000 \\ 1534253832926700000000000000 & 1917817291158375000000000000 & 33370020866155725000000000000 & 2684944207621725000000000000 \end{array}]$