PreCalculus Section 14.3 Solve linear equations using matrices

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Presentation transcript:

PreCalculus Section 14.3 Solve linear equations using matrices [A] + [Z] = [A] 2 5 4 3 + 0 0 0 0 = 2 5 4 3 [A] · [I] = [A] 2 5 4 3 · 𝟏 0 0 𝟏 = 2 5 4 3 [A] · [A]-1 = [I] 2 5 4 3 · −𝟑/𝟕 𝟓/𝟏𝟒 𝟐/𝟕 𝟏/𝟕 = 𝟏 𝟎 𝟎 𝟏 Note: many of the properties of real numbers and matrices are similar. Real numbers a + 0 = a a · 1 = a a(1/a) = 1

Linear equations and matrix equations can be solve in similar fashions. AX = B 3 2 7 5 X = 9 3 9 1 A-1 A X = A-1 B

Solve the matrix equation

A system of linear equations can be written as a matrix equation. 5x + 4y = -2 2x + 3y = -5

Solve the system 2x - y + z = 3 3x + 2y – 4z = 23 x – 3y – 2z = 14

Page 536 problem 25

Assignment Page 534 Problems 2,4 10,12,14,16,23,26a