Question

can anyone please help me with my algebra worksheet? Pic attached.

Answer 1

To find the sum of two matrices, just add the numbers that are at the same position in both the matrices. So for the first question you will add the following numbers:
-308 + 105 = -203
651 + 318 = 969
and so on for all the four pairs of numbers

Answer 2

okay so those two^ and then 912+ -762=150 and -347+ -438=-785

Answer 3

right

Answer 4

so my answer is

Answer 5

Yes that is the answer good!

Answer 6

now how do i do the next two??

Answer 7

Okay first lets solve b because it will help you solve a.

To find the determinant of the matrix in b, just cross mulitply the numbers and subtract them. So you get

-1*2 - 5*3

Remember to multiply the numbers in the principle diagonal first.

Answer 8

So the determinate of the matrix in b is -2 - 15 = -17

Answer 9

thats it?

Answer 10

yes

Answer 11

but then the first one is so much harder cause theres a whole other row... :(

Answer 12

Yes let me explain

Answer 13

okay

Answer 14

Consider the first row having the numbers -2, 4 and 1.

Take the number -2. Now hid the row and column of numbers of which -2 is a part. This leaves four numbers in the form of a matrix,
\[\left[\begin{matrix}0 & -1 \\ 2 & 1\end{matrix}\right]\]
Find the determinant of the above matrix. It is 0*1 - -1*2 = 2
Multiply the number -2 taken above with the determinant 2 so you get -2 * 2 = 4.

Answer 15

Now we repeat the process with number 4 in the first row
Hide the row and column of which 4 is a part so you are left with four numbers in the form of a matrix:
\[\left[\begin{matrix}3 & 1 \\ -1 & 1\end{matrix}\right]\]
Its determinant is 4. Multiply the number 4 above with the determinant 4 to get 16.

Answer 16

Do the same with the third number in the first row, 1. When you hide its row and column, the determinant of the remaining matrix is 6. Multiply 1 and 6 to get 6.

Now add the three values we got for each number but remember that the value for the middle number 4 is subtracted not added.

so you get 4 - 16 + 6 = -6

Answer 17

do you know how to determine if a matrix has an inverse? can you help me with that too? if not, thanks for what you did help with, it means a lot!

Answer 18

idk how to make a matrix on here but i have
[4 8
-3 -2]

Answer 19

and [6 -8
-3 4]

Answer 20

and it asks to determine whether each matrix has an inverse and if it does to find it

Answer 21

A matrix doesn't have an inverse if its determinant is zero so find the determinants of each matrix and if it is zero, then the matrix does not have an inverse

Answer 22

okay thanks!!!

Answer 23

the determinant for the first one is 16, so is that the inverse too? or

Answer 24

@navk

Answer 25

Since the determinent of the first is 16 that means it has an inverse

Answer 26

how do i find the inverse? or did i do that?

Answer 27

To find the inverse, exchange the numbers on the principle diagonal, change the sign on the numbers not on the principle diagonal, and then divide each number by the determinant. This gives you
\[\frac{ 1 }{ 16 }\left[\begin{matrix}-2 & 4 \\ 3 & -8\end{matrix}\right]\]

Answer 28

Note that the above procedure applies only two 2x2 matrices, not to 3x3 or higher matrices.

Answer 29

this is hard LOL. ok then do i just solve that^?