[PDF] CHAPTER 8: MATRICES and DETERMINANTS

Determinants of Matrices - Montgomery College

For higher rank matrices, we can use cofactors to calculate their determinants: The cofactor of an element in row I and column J is the determinant of the matrix that remains after row I and column J are removed:

CHAPTER 8 Matrices and Determinants

Matrices and Determinants Section 8 1 Matrices and Systems of Equations You should be able to use elementary row operations to produce a row-echelon form (or reduced row-echelon form) of a matrix 1 Interchange two rows 2 Multiply a row by a nonzero constant 3 Add a multiple of one row to another row

MATRICES: DETERMINANTS - University of Sheffield

MATRICES: DETERMINANTS 5 minute review Remind students how to compute determinants (both 2 2 and 3 3) In the 3 3 case, explain that you can use di erent rows or columns As an example, you could show that jAj= 6 and jBj= 3 for the matrices below A = 1 2 3 0 ; B = 2 4 4 13 4 0 1 1 3 7 5 3 5: Class warm-up

CHAPTER 8: MATRICES and DETERMINANTS

(Section 8 1: Matrices and Determinants) 8 07 3) Row Replacement (This is perhaps poorly named, since ERO types 1 and 2 may also be viewed as “row replacements” in a literal sense ) When we solve a system using augmented matrices, We can add a multiple of one row to another row Technical Note: This combines ideas from the Row Rescaling ERO

Matrix algebra for beginners, Part I matrices, determinants

Determinants & Inverse Matrices

Determinants & Inverse Matrices The determinant of the 2⇥2matrix ab cd is the number adcb The above sentence is abbreviated as det ab cd = adcb

Determinants, part II Math 130 Linear Algebra

Determinants, part II Math 130 Linear Algebra D Joyce, Fall 2013 So far we’ve only de ned determinants of 2 2 and 3 matrices The 2 2 determinants had 2 terms, while the determinants had 6 terms There are many ways that general n n determinants can be de ned We’ll rst de ne

Determinants of 2×2 Matrices Date Period - Kuta Software LLC

Determinants of 2×2 Matrices Date_____ Period____ Evaluate the determinant of each matrix 1) 0 −4 −6 −2 −24 2) −6 0 6 −6 36 3) −1 1 −1 4 −3 4) 0 4 6 5 −24 5) 0 −1 6 −6 6 6) 5 3 6 6 12 Evaluate each determinant 7) −5 3 4 2 −22 8) −9 −9 −7 −10 27 9) −1 8 5 0 −40 10) 8 −6 −10 9 12 11) 0 6 −8 0 48 12