Use row reduction to find the inverse of the given matrix if it exists, and check your answer by multiplication.
2 answers:
Answer:
Step-by-step explanation:
Given the 2×2 matrix since the matrix consists of 2rows and 2columns, to find its inverse using row reduction method, we will augment the matrix given with a 2×2 identity matrix before carrying out the reduction on the resulting 2×4 matrices. The resulting matrix must be an identity matrix augmented with the inverse of the matrix in question. The process of reduction is as shown in simple steps.
[A | I] -> [I | A-¹] where
A is the given matrix
I is the 2×2 identity matrix
A-¹ is the inverse of the matrix
Check attachment for the reduced matrix.
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There's no if about it,
has a zero
so 
is a factor. That's the special case of the Remainder Theorem; since we'll get a remainder of zero when we divide 
by 
At this point we can just divide or we can try more little numbers in the function. It doesn't take too long to discover
too, so 
is a factor too by the remainder theorem. I can find the third zero as well; but let's say that's out of range for most folks.
So far we have
where
is the zero we haven't guessed yet. Again we could divide by 
but just looking at the constant term we must have
so
We check
We usually talk about the zeros of a function and the roots of an equation; here we have a function whose zeros are
has a zero
At this point we can just divide or we can try more little numbers in the function. It doesn't take too long to discover
So far we have
where
so
We check
We usually talk about the zeros of a function and the roots of an equation; here we have a function