3. Find the inverses of the following matrices, if they...

3. Find the inverses of the following matrices, if they exist. $A = \begin{bmatrix} 5 & 10 \\ 4 & 7 \end{bmatrix}$, and $B = \begin{bmatrix} 1 & -2 & 1 \\ 4 & -7 & 3 \\ -2 & 6 & -4 \end{bmatrix}$.

Transcript

00:01 We have given in the question a is equal to 2, 5, 1 minus 3, find a inverse.

00:05 Now we can say if we have given a is equal to a, b, c, d, then a inverse becomes 1 divided by a, 1 divided by a, and here d minus d minus c and a.

00:24 It is d minus b minus b and a now we can say a inverse becomes a inverse becomes one upon minus 11 1 upon 1 divided by minus 11 minus 3 minus 5 minus 1 and 2 minus 1 and 2 it is we can say it means it is minus 1 divided by 11 and 11 and it is minus 3 minus 3 minus 5 minus 1 and 2 and 2 now we know that a and a inverse if we can multiply of them it is equal to i it is equal to i now i is equal to becomes i becomes becomes minus 1 divided by 11 minus 1 divided by 11 2 5 to 5 1 minus 1 minus 3 251 minus 3 and multiply by minus 3 minus 5 minus 1 and minus 2.

01:35 Minus 1 and minus 2.

01:37 Now we can do the multiple of them and it becomes minus 1 divided by 11 and it becomes 2 multiply by minus 3 becomes minus 3 becomes minus 6.

01:50 Multiply here we can say it is becomes minus 5 and minus 10 plus 10 minus 10 plus 10 and it is become minus 3 plus 3 and it is minus 5 minus 5 minus 6 now we can say i is equal to minus 1 divide by 11 becomes minus 6 minus 5 minus 5 becomes minus 11 and minus 10 plus 10 becomes 0 and minus 3 plus 3 becomes 0 and minus 5 minus 6 becomes minus 11 now we can to do here common minus 11 if we can do the minus 11 now here the 5 becomes i becomes 1 0 and 0 1 now we can say a inverse is equal to a inverse is equal to minus 1 divided by 11 minus 3 minus 5 minus 1 minus 2 and this is our answer firstly this is our answer the inverse becomes this a inverse is this now we are going to option b and option b we have given option b we have given if a is equal to if a is equal to 4 3 minus 2 4 3 minus 2 3 1 minus 3 1 minus 3 and minus 1 minus 2 4 minus 2 and plus 4 minus 2 and plus 4 inverse becomes a inverse becomes 1 phone a adjacent of a here here b is equal to this is the b and b is equal to 4 4 minus 6 4 minus 6 4 is here and 1 multiply 4 become 4 minus 2 multiply by minus 3 becomes minus 6 and minus 3 now minus 3 multiply by minus 1 and minus 3 becomes plus 3 and 3 multiply by 4 becomes 12 minus 3 we can say it is minus 2 multiply by minus 6 plus 1 and 3.

04:21 This is the minus 2 multiply by 4 becomes minus 8 here 9 minus 3 becomes minus 27 plus 10 and d is equal to here minus 25 the value of d is equal to that vector d is equal to 25 now we are going a11 we are find a11 is equal to a11 is equal to a1 1 1 is equal to positive 1 minus 3 minus 2 4 1 minus 3 minus 2 and plus 4 and a 1 2 is equal to a 1 2 is equal to a 1 2 minus 3 minus 3 minus 1 and 4 and a 1 3 is equal to b 1 3 1 minus 1 minus 2 minus 2 now a 2 1 1 is equal to we have to find a 2 -1 and a 2 -1 is equal to minus 3 minus 2 minus 2 4 and a -2 is equal to and a -2 -2 and a -2 -2 -4 minus 2 minus 1 and 4 minus 2 minus 1 and 4 a 2 3 is equal to a 2 3 is equal to it becomes minus 4 minus 2 3 and minus 3 3 and minus 3.

05:53 Now we can find a31 and a31 is equal to positive 3 minus 2 and 1 minus 3.

06:03 1 minus 3...

Question

3. Find the inverses of the following matrices, if they exist. $A = \begin{bmatrix} 5 & 10 \\ 4 & 7 \end{bmatrix}$, and $B = \begin{bmatrix} 1 & -2 & 1 \\ 4 & -7 & 3 \\ -2 & 6 & -4 \end{bmatrix}$.

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