Identity matrices , inverses and determinants of square matrices, including IM=MI=M, the inverse condition detM=0⟺M−1
The identity matrix I is a square matrix with 1s along its top-left to bottom-right diagonal, and 0's everywhere else. When multiplied by any matrix with appropriate order, the product is the same matrix:
The inverse of a matrix is the matrix M−1 that when multiplied by M gives the identity.
If M=(acbd), then
A square matrix M is invertible if and only if its determinant is non-zero:
If the matrices A and B are invertible, then
This result is found by left-multiplying (remember for matrices order of multiplication matters) by A−1 or right-multiplying by B−1.
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.
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 det(. Type
and the calculator will spit out the determinant.
Nice work completing Identity, Inverses & Determinants, here's a quick recap of what we covered:
Exercises checked off
Identity matrices , inverses and determinants of square matrices, including IM=MI=M, the inverse condition detM=0⟺M−1
The identity matrix I is a square matrix with 1s along its top-left to bottom-right diagonal, and 0's everywhere else. When multiplied by any matrix with appropriate order, the product is the same matrix:
The inverse of a matrix is the matrix M−1 that when multiplied by M gives the identity.
If M=(acbd), then
A square matrix M is invertible if and only if its determinant is non-zero:
If the matrices A and B are invertible, then
This result is found by left-multiplying (remember for matrices order of multiplication matters) by A−1 or right-multiplying by B−1.
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.
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 det(. Type
and the calculator will spit out the determinant.
Nice work completing Identity, Inverses & Determinants, here's a quick recap of what we covered:
Exercises checked off