620 views

### How does one find the inverse of a non-singular 3x3 matrix A?

(i) Find the DETERMINANT of A:

1. Multiply the (1,1)th element by the determinant of the 2x2 matrix that remains when the row and the column containing the element are crossed out.

2. Repeat for the elements (1,2)th and (1,3)th elements.

3. Alternately add and subtract the results.

(ii) Find the ADJUGATE of A (also known as the classical adjoint of A):

1. Form M, the matrix of minors of A, where the minor of an element of a 3x3 matrix is the determinant of the 2x2 matrix that remains when the row and the column containing the element are crossed out.

2. Form C, the matrix of cofactors, by changing the signs of alternating elements of M starting with the top left element as positive.

3. Form adj(A) = C^T, the transpose of the matrix of cofactors, by reflecting the matrix about the main diagonal (i.e. swapping the (i,j)th element with the (j,i)th element.)

(iii) Find the INVERSE of A, given by

where det(A) us the determinant of A and adj(A) is the adjugate of A.

NB: The same method can also be applied to larger square matrices but the process is long so instead we use the Guass-Jordon Method of Elimination, which is also applicable to 3x3 matrices.

1 year ago

Answered by Anya, an A Level Maths tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 360 SUBJECT SPECIALISTS

£22 /hr

Degree: Electrical and Electronic Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“I am passionate, motivated, and always hungry for more knowledge. I can bring energy and life to the classroom, and engage the student.”

£26 /hr

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Premium tutor. First class graduate with teaching experience from a top Russell Group university. I deliver fun and relaxed lessons which achieve results!”

£22 /hr

Degree: Mathematics (Bachelors) - Imperial College London University

Subjects offered:Maths

Maths

“21 years old. 2 years experience teaching. BSc Mathematics Imperial College London. Studying MSc in Aerospace Dynamics (please ask for references).”

Currently unavailable: for regular students

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths

Maths

“Hi! My name is Anya and I’m a 2nd year Mathematics student at the University of Bristol. I’m afriendly and patient individual, excited for the opportunity to aid pupils in the advancement of their mathematicalfluency and confidence, a...”

### You may also like...

#### Posts by Anya

How does one find the derivative of ln(x)?

How does one find the highest common factor (HCF) and lowest common multiple (LCM) of 36 and 48?

How does one find the inverse of a non-singular 3x3 matrix A?

How does one show that x^2 + x + 1 > 0 for all values of x?

#### Other A Level Maths questions

Find the X-coordinates of the stationary points on the graph with equation y = f(X), where f(X) = X^3 + 3X^2 -24X.

The equation of a curve is x(y^2)=x^2 +1 . Using the differential, find the coordinates of the stationary point of the curve.

How do I do binomial expansions for positive integer n?

G(x)=x^3 + 1, h(x)=3^x; solve G(h(a))=244

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.