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This document provides math problems involving determinants and systems of linear equations for students to solve. It includes: 1) Calculating determinants of second and third order. 2) Solving systems of linear equations using Cramer's Rule. 3) Noting the problems should be done on paper, following proper order of operations. Students are to show their work and solutions.
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5 b
This document contains math problems involving determinants of second and third order, and solving systems of linear equations. It asks the student to:
1) Calculate 6 determinants of second order.
2) Calculate 5 determinants of third order using Sarrus' method.
3) Solve 6 systems of linear equations using Cramer's rule.
Matematica de 5to
Este documento presenta el tema de álgebra matricial para estudiantes de quinto año de bachillerato técnico en matemáticas V. El tema incluye conceptos como matrices, sus orígenes, aplicaciones, notación, tipos y operaciones, así como determinantes, su concepto, orden, notación, diagonal principal y secundaria, propiedades, métodos de Sarrus y Cramer.
Algebra
Este documento presenta una introducción a las matrices y los determinantes en el álgebra. Cubre los conceptos básicos de las matrices, incluida su notación, tipos y operaciones, así como sus aplicaciones en la vida diaria. También explica los conceptos clave de los determinantes, como su orden, notación, propiedades y métodos para calcularlos, como el método de Sarrus y la regla de Cramer.
Conceptos generales trigonometria
Este documento presenta conceptos generales de trigonometría. Explica sistemas de coordenadas rectangulares, el concepto de radio vector y la aplicación del teorema de Pitágoras. También define las funciones trigonométricas básicas y explica cómo calcular las funciones para ángulos mayores de 90 grados usando ángulos relacionados. Además, proporciona fórmulas para calcular las funciones trigonométricas de ángulos especiales como 30, 45, 60 y 90 grados.
Sistemas de ecuaciones lineales con dos y tres
The document discusses systems of linear equations with two and three unknowns. It begins by explaining the origins of solving systems of equations dating back to ancient Egyptians, Greeks, Indians, and Babylonians. It then provides examples of applications of systems of linear equations in fields like engineering, physics, biology, and economics. Finally, it discusses different methods that can be used to solve systems of linear equations like substitution, elimination, and graphing.
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5 a
- 1. INSTITUTO TECNOLOGICO SAN IGNACIO DE LOYOLA (ITESIL) Facilitadora: Altagracia Belliard
- 2. Realizaloque se te pide a continuación: a) Calcula los siguientesdeterminantes de segundoorden. 1. ⌈ 𝟏 𝟕 𝟗 −𝟐 ⌉ 2. ⌈ −𝟐 𝟓 𝟑 𝟖 ⌉ 3. ⌈ 𝟏 −𝟑 𝟒 −𝟕 ⌉ 4. ⌈ 𝟏𝟎 𝟗 −𝟐 𝟑 ⌉ 5. ⌈ −𝟒 −𝟓 𝟑 𝟐 ⌉ b) Calcular los siguientes determinantesde tercer ordenaplicandoel métodode sarrus. 1. ⌈ 𝟐 −𝟏 𝟐 𝟏 𝟑 𝟏 𝟒 −𝟐 𝟓 ⌉ 2. ⌈ 𝟏 𝟐 −𝟐 −𝟏 𝟓 𝟎 𝟒 −𝟑 −𝟓 ⌉ 3. ⌈ 𝟏𝟎 −𝟑 𝟓 −𝟏 𝟐 𝟑 −𝟔 𝟒 −𝟐 ⌉ 4. ⌈ 𝟏 −𝟑 𝟐 𝟐 −𝟏 −𝟏 𝟏 𝟏 −𝟑 ⌉ 5. ⌈ 𝟏 𝟐 𝟑 𝟑 𝟐 𝟏 𝟏 𝟏 𝟏 ⌉
- 3. c) Resuelve los siguientes sistemas de ecuaciones linealesaplicando la reglade Cramer 1. { 𝟐𝒙 − 𝒚 = −𝟗 𝒙 + 𝟐𝒚 = 𝟖 } 2. { 𝟔𝒙 + 𝟏𝟐𝒚 = 𝟑𝟑 𝟒𝒙 + 𝟕𝒚 = 𝟐𝟎 } 3. { 𝒙 + 𝒚 − 𝒛 = 𝟔 𝟑𝒙 − 𝟐𝒚 + 𝒛 = 𝟎 𝒙 + 𝟑𝒚 − 𝟐𝒛 = 𝟏𝟒 } 4. { 𝟑𝒙 + 𝟓𝒚 = 𝟏 −𝒙 + 𝟐𝒚 = 𝟕 } 5. { 𝟑𝒙 − 𝟐𝒚 + 𝟓𝒛 = 𝟏𝟒 𝒚 − 𝟒𝒛 = −𝟏𝟎 𝟐𝒚 + 𝒛 = 𝟕 } 6. { 𝒙 − 𝒛 − 𝒚 = −𝟒 𝟐𝒙 − 𝟑𝒚 + 𝟒𝒛 = −𝟏𝟓 𝟓𝒙 − 𝟐𝒛 + 𝒚 = 𝟏𝟐 } Nota:Esta actividades para realizarlaentulibretade apunte o cuadernos. Al momento de realizar cada ítems debe de tener en cuentala jerarquíade las operaciones.