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2.5 - Determinants & Multiplicative Inverses of Matrices

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DETERMINANT a real number representation of a square matrix. The determinant of is a number denoted as or det a matrix with a nonzero determinant is called nonsingular

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Second-Order Determinant The value of det or is ad - cb.

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Examples 1. Find the value of 2. Find the value of 0(-6) - 8(-2) = 16 8(6) - 7(4) = 20

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page 98

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Third-Order Determinant

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Find the value of

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Option 2 for finding 140 + 0 + 18 - 0 - -120 - 126 = 152

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The Identity Matrix a square matrix whose elements in the main diagonal, from upper left to lower right, are 1s, while all other elements are 0s.

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Inverse Matrix the product of a matrix and it’s inverse produces the identity matrix only for square matrices The inverse of matrix A would be denoted as A -1

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Inverse of a Second-Order Matrix First, the matrix must be nonsingular! Then, if the matrix is nonsingular, an inverse exists. If the detA = 0, then it is singular and no inverse exists.

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Inverse of a Second-Order Matrix If A = and, then A -1 =

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Find the inverse of 1st - find the det 8(-1) - 3(9) = -35 2nd - find the inverse or

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DAY 2

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Let’s use some technology! it is important that you know how to do all these operations by hand. matrices bigger than a second order are time consuming and well as multiplying matrices. your calculators do all of this, but remember you will have a non-calculator section of your test.

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are solving systems and matrices in the same chapter? You can use inverse matrices to solve systems of linear equations!

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If we rewrite the system as a product of matrices: Now, if this were a simple linear equation, like 5x = 15, how would you “get rid of” the 5?

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First, find the inverse of Then, multiply both sides by the inverse. (5, 2)

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Use inverse matrices to solve

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