Question

I need to find the missing numbers

Answer 1

b11 = -14

b12 = 9

b13 = 8

Explanation:

* Lets revise some notes to solve the problem

- Any matrix has a dimension m × n, where m is the number of rows

and n the number of columns

- We can add matrices with same dimensions

* Now lets solve the problem

∵
`B+\left[\begin{array}{ccc}15&-7&4\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}1&2&12\\4&0&2\end{array}\right]`

- Let
`B=\left[\begin{array}{ccc}b11&b12&b13\\b21&b22&b23\end{array}\right]`

∴
`\left[\begin{array}{ccc}b11&b12&b13\\b21&b22&b23\end{array}\right]+\left[\begin{array}{ccc}15&-7&4\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}1&2&12\\4&0&2\end{array}\right]`

- Lets add and find the missing

* Lets start with the first rows

∵ b11 + 15 = 1 ⇒ subtract 15 from both sides

∴ b11 = -14

∵ b12 + -7 = 2 ⇒ add 7 to both sides

∴ b12 = 9

∵ b13 + 4 = 12 ⇒ subtract 4 from both sides

∴ b13 = 8

* Now lets start with the second rows

∵ b21 + 0 = 4

∴ b21 = 4 ⇒ given

∵ b22 + 1 = 0 ⇒ subtract 1 from both sides

∴ b22 = -1 ⇒ given

∵ b23 + 2 = 2 ⇒ subtract 2 from both sides

∴ b23 = 0 ⇒ given