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Determinant The numerical value of a square array of numbers that can be used to solve systems of equations with matrices. Second-Order Determinant (of a 2 x 2 Matrix) The word with the matrix symbol The Determinant symbol (Criss-Cross & multiply then subtract)

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Example 1

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nth-Order Determinant The determinant of any n x n (square) matrix Third-Order Determinant (of a 3 x 3 Matrix) Determinant of what’s left Signs alternate, beginning with minus Then simplify

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Example 2 Select any row & column, then calculate the determinant with expansion of the minors

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Identity Matrix for Multiplication A square matrix, that when multiplied with another square matrix, results in a matrix with no change. The square matrix always consists of 1’s on the diagonal beginning with the first element; the remaining elements are zeros.

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Inverse Matrix (A -1 ) A matrix that when multiplied by another matrix results in the identity matrix. Note: Not all matrices have an inverse – If the determinant of the original matrix has a value of zero, A -1 does not exist

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Example 3 Determine if a matrix exists (Det ≠ 0) 4 2 3 -4 Switch places Same place Switch Signs The inverse is used to solve systems of equations with matrices.

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Calculate the determinant: Determine the inverse: Multiply each side of the matrix equation by the inverse & solve:

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Example 5 Define the variables: Let x = amount of 10% bond Let y = amount of 6% bond Two variables, two equations: x + y = 10,500 Simplify; no decimals. Write matrix equation:Determine the inverse: 1(-5) – 3(1) = -8 3x – 5y = 0

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HW: Page 102

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SHOP ATVRADIO DAY 153 DAY 278 DAY 345 SHOP BTVRADIO DAY 194 DAY 285 DAY 363 TOTALTVRADIO DAY 1147 DAY 21513 DAY 3108 This can be written in matrix form.

SHOP ATVRADIO DAY 153 DAY 278 DAY 345 SHOP BTVRADIO DAY 194 DAY 285 DAY 363 TOTALTVRADIO DAY 1147 DAY 21513 DAY 3108 This can be written in matrix form.

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