what is the inverse of -3 4
-4 8?
What do you mean by inverse?
The inverse is switching the numerator and the denominator. For example the inverse of 3/4 is 4/3.
Also I searched Google under the key word "inverse" to get these possible sources:
http://en.wikipedia.org/wiki/Inverse_function
http://www.merriam-webster.com/dictionary/inverse
http://www.purplemath.com/modules/invrsfcn.htm
http://en.wiktionary.org/wiki/inverse
http://en.wikipedia.org/wiki/Inverse_(mathematics)
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
I hope this helps. Thanks for asking.
To find the inverse of a 2x2 matrix, you can follow these steps:
Step 1: Write down the given matrix:
-3 4
-4 8
Step 2: Determine the determinant of the given matrix:
The determinant of a 2x2 matrix 𝐴 = |𝑎 𝑏|
|𝑐 𝑑|
is given by the formula: 𝑑𝑒𝑡(𝐴) = 𝑎𝑑 − 𝑏𝑐
So, for our given matrix, the determinant (𝑑𝑒𝑡) = (-3 * 8) - (4 * -4) = -24 + 16 = -8.
Step 3: Check if the matrix is invertible:
In order for a matrix to have an inverse, the determinant cannot be equal to zero. Since the determinant in this case is -8, which is not zero, the given matrix is invertible.
Step 4: Find the adjugate matrix:
The adjugate of a 2x2 matrix 𝐴 = |𝑎 𝑏|
|𝑐 𝑑|
is obtained by swapping the diagonals and changing the sign of the off-diagonals, which gives us:
𝑎𝑑𝑗(𝐴) = |𝑑 -𝑏|
|-𝑐 𝑎|
Therefore, the adjugate of our given matrix is:
𝑎𝑑𝑗(𝐴) = |8 -4|
|4 -3|
Step 5: Calculate the inverse matrix:
Finally, we can calculate the inverse of the matrix by dividing the adjugate matrix by the determinant, like this:
𝐴^(-1) = (1/𝑑𝑒𝑡(𝐴)) * 𝑎𝑑𝑗(𝐴)
Substituting the previously calculated values, we have:
𝐴^(-1) = (1/-8) * |8 -4|
|4 -3|
Simplifying further, we get:
𝐴^(-1) = |-1/8 1/4|
|-1/2 3/8|
So, the inverse of the given matrix:
-3 4
-4 8
is:
|-1/8 1/4|
|-1/2 3/8|