Good day students welcome to mathgotserved.com in this clip were going to be going over how
to find and verify inverse a square matrix forget to visit our website at mathgotserved.com
for access to a wide variety of tutorials ranging from algebra and calculus so we only
get started let's go over what the formula is finding the inverse of the matrix okay
so the formula you matrix a square 2 x 2 matrix is a b c d Dan -1 is going to be one over
the determinant of a multiplied by what you gets we take the industries the diagonals
DA and take the opposite of the week negative see negative okay so this is the formula for
finding the then the inverse the inverseof the matrix I don't forget that's the determinant
of matrix a is given by 4 x 2 matrix it is a product of the diagonal a D this is the
diagonal right here ab minus the product on the way to the wings right here DC okay you
want to note in the determinant of a is equal to zero guess what then eight to that into
the negative one is not to find so that if the degrees tells us that the matrix is not
vertical if it has is zero determine what I that the inverse only matrix to determine
it was never be zero okay so let's keep that in mind go ahead and try example 1 so we are
to find the inverse and verify that our answer is correct okay so why inverse it is negative
one and verify your answer where all matrix a is equal to 2143 okay so
there goes your matrix a isolate and find the inverse first remember the full authority
inverse it's one over a D minus DC 100 and determinant isolate you get when you switch
the diagonals DA 18 the opposite of the wings needed be negative see I so let's see what
easy and the artist is a right here a the see the simplify the inverse relationship
the following are going to do one over 8080 is 2×3 which is six minus DC which is for
multiplied byif we switch a and d will have three to and opposite of one for your one
and name for I we were further will have one over to times three -4 -1 2000 is simply distributes
to into the entire into the elements of this matrix so can distribute to the one half we
have three over to minus forward to minus one over to and then positive to over to the
reduced form of this matrix is three over to -2 minus one half into over to is one so
this is my inverse a today negative one were also asked to verify that our solution is
correct to accomplish this with going to do a check in our check is in in most multiplying
a of this inverse and that she give us the identity major so let's see that's what happens
here matrix eight this rewrite matrix is to one or three and matrix the only a inverse
right is three over two negative one half negative to and one so want to see the product
of these two is equal to the identity matrix? Is it equal to the identity matrix 1001 this
is the identity matrix for 2 x 2 matrix now let's go ahead and multiply and set up my
multiplication bars I like to multiply using a different method so on when a line with
my rules of this colony; in this right here so my rules from matrix a to come of four
and then the second row one, three negative take my my columns from matrix the inverse
and line them up horizontally so we have three over to, negative one half and -2, one okay
so what is going to just multiply X is an wise and by the sum so three over to times
two is 3+ negative one half times four is positive actually negative negative to be
-2 is one of multiply these two make coordinates -2 times positive to the -41×4 is for the
sum is it to this to one faster over to the to three that's negative one half -3 over
to the sum is zero and then the last set one and negative to is negative to 1×303 the
sum is one so we can see that the product off a and the resulting dots resulted in the
identity matrix so with confidence that our solution is in fact correct okay so let's
talk our answer a inverse equals three over to negative to negative one half and one so
that's that the thanks so much for taking the time to
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