Identity, Inverses & Determinants
The concept of an identity matrix and inverse matrices, and determinants. Finding inverses with technology, or by hand for โ(2ร2)โ matrices
Want a deeper conceptual understanding? Try our interactive lesson!
Identity Matrix
The identity matrix โIโ is a square matrix with โ1โs along its top-left to bottom-right diagonal, and โ0โ's everywhere else. When multiplied by any matrix with appropriate order, the product is the same matrix:
Definition of the inverse matrix
The inverse of a matrix is the matrix โMโ1โ that when multiplied by โMโ gives the identity.
Inverse of a 2 by 2 matrix by hand
If โM=(acโbdโ), then
Determinant of 2 by 2 matrix by hand
Existence of the inverse
A square matrix โMโ is invertible if and only if its determinant is non-zero:
Operations using inverses: AB=C โน B=AโปยนC, A=CBโปยน
If the matrices โAโ and โBโ are invertible, then
Inverse of a matrix using technology
You can find the inverse of any (square) matrix on your calculator. Enter your matrix into your calculator, for example in [A], and then simply type
and the calculator will spit out the inverse, if it exists.
Determinant of a matrix using technology
You can find the determinant of any (square) matrix on your calculator.
Enter your matrix into your calculator, for example in
[A].Under the matrix menu, you will find a bunch of functions, the first of which should be โdet(. Type
and the calculator will spit out the determinant.
Nice work completing Identity, Inverses & Determinants, here's a quick recap of what we covered:
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