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Graphing Calculator by Mathlab: User Manual
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  • Home
    • Introduction
    • PRO Features vs. FREE Version
    • Frequently Asked Questions, FAQs >
      • 1. How to Change the Number Format?
      • 2. How to Set Up the Separators Between Thousands?
      • 3. How to Set Precision?
      • 4. How to Send Feedback with Comments?
      • 5. How to import/export the library?
      • 6. How to Print Results?
      • 7. How to Make the Calculator Show the Results?
      • 8. How to Transport Calculation Results to other Programs?
      • 9. How to Transport Table to Other Platforms?
      • 10. How to Turn Off (or on) Vibration?
      • 11. How to Change the Language?
  • 1. Basics
    • 1.1. Navigation
    • 1.2. UI Elements
    • 1.3. Keyboard
    • 1.4. Input, Enter, Delete, Clear and UNDO Buttons
    • 1.5. Workspace Area
    • 1.6. Editing the Expression/Equation
    • 1.7. Using the Last Answer
    • 1.8. Writing Comments
    • 1.9. Clear, Copy & Paste Commands
    • 1.10. Rearranging Rows
  • 2. Settings
    • 2.1. General
    • 2.2. Calculator
    • 2.3. Graph
  • 3. Library
    • 3.1. Constants
    • 3.2. Functions
    • 3.3. How to Save Calculation Result/Graph to Library?
  • 4. Graph Mode
    • 4.1. 2D Graphing
    • 4.2. 3D Graphing
    • 4.3. Enlarging the Graph Area
    • 4.4. Changing to White Background
    • 4.5. Hide Keyboard
    • 4.6. Degree and Radian Scales
    • 4.7. Fixed Scale
    • 4.8. R-axis Scale
    • 4.9. Logarithmic Scale
    • 4.10. Tracing Values and Slopes
    • 4.11. Special Points: Roots and Criticals
    • 4.12. Intersections of Graphs
    • 4.13. Set Domain
    • 4.14. Show All - Roots, Critical Points and Intersections
    • 4.15. Fullscreen
  • 5. Table Mode
    • 5.1. Sharing of Functions
    • 5.2. 2D Table
    • 5.3. 3D Table
    • 5.4. Edit Functions
    • 5.5. Scroll Results
    • 5.6. Results Precision
    • 5.7. Zoom Controls
    • 5.8. Save and Load Table
    • 5.9. Table of Trigonometric Functions
  • 6. Numbers and Number Sense
    • 6.1. Decimals
    • 6.2. Fractions >
      • 6.2.1. Mixed Fractions
      • 6.2.2. Complex Fractions
      • 6.2.3. Converting Decimals to Fractions
      • 6.2.4. Converting Fractions to Decimals
    • 6.3. Percents
    • 6.4. Scientific Notation
    • 6.5. Engineering Notation
    • 6.6. Rounding Numbers
    • 6.7. Integer and Fractional Parts >
      • 6.7.1. Integer Part of a Number >
        • 6.7.1.1. Ceiling
        • 6.7.1.2. Floor
        • 6.7.1.3. Half Down
        • 6.7.1.4. Half to Even
        • 6.7.1.5. Half to Infinity
        • 6.7.1.6. Half to Odd
        • 6.7.1.7. Half to Zero
        • 6.7.1.8. Half Up
        • 6.7.1.9. Truncate
      • 6.7.2. Greatest Integer is the Floor Function
      • 6.7.3. Least Integer is the Ceiling Function
      • 6.7.4. Fractional Part of a Number
    • 6.8. Order of Operations
    • 6.9. Least Common Multiple
    • 6.10. Greatest Common Divisor
    • 6.11. Modulo
    • 6.12. Binary, Octal, Decimal, Hexadecimal Numbers
    • 6.13. Complex Numbers
    • 6.14. The Polar Form of Complex Numbers
    • 6.15. Polar to Rectangular Coordinates
  • 7. Introductory Algebra
    • 7.1. Arithmetic Operations
    • 7.2. Exponents
    • 7.3. Absolute Values
    • 7.4. Variables
    • 7.5. Evaluating Expressions
    • 7.6. Polynomials
    • 7.7. Roots
    • 7.8. Logarithms
  • 8. Equations in One Variable
    • 8.1. Linear Equation
    • 8.2. Absolute Value Equation
    • 8.3. Quadratic Equation
    • 8.4. Cubic Equation
    • 8.5. Polynomial Equation
    • 8.6. Rational Equation
    • 8.7. Radical Equation
    • 8.8. Exponential Equation
    • 8.9. Logarithmic Equation
  • 9. Inequalities in One Variable
    • 9.1. Inequality Symbols
    • 9.2. Linear Inequalities
    • 9.3. Absolute Value Inequalities
    • 9.4. Quadratic Inequality
    • 9.5. Polynomial Inequalities
    • 9.6. Rational Inequalities
    • 9.7. Compound Inequalities
    • 9.8. Inequalities with Constants
  • 10. Equations and Inequalities in Two Variables
    • 10.1. Linear Equations
    • 10.2. Systems of Linear Equations
    • 10.3. Graphing Inequalities
    • 10.4. Multiple Graphing of Inequalities
    • 10.5. Graphing Systems of Inequalities
    • 10.6. Solving Implicit Equations
  • 11. Algebraic Functions and Graphs
    • 11.1. Plotting Points
    • 11.2. How to Graph Functions?
    • 11.3. Setting the Applied Domain
    • 11.4. Linear Function
    • 11.5. Absolute Value Function
    • 11.6. Quadratic Function
    • 11.7. Polynomial Functions
    • 11.8. Rational Functions
    • 11.9. Radical Functions
    • 11.10. Logarithmic Functions
    • 11.11. Exponential Functions
    • 11.12. Sign Function
    • 11.13. Multiple Graphing
    • 11.14. Piecewise Functions
  • 12. Matrices and Vectors
    • 12.1. Matrix Operations
    • 12.2. Editing Matrix Entries
    • 12.3. Matrix Variables
    • 12.4. Matrix and Vector Forms
    • 12.5. Variable Matrix to System of Linear Equations
    • 12.6. Solving Systems of Linear Equations Using Matrix Equations
  • 13. Trigonometric Functions and Their Inverses
    • 13.1. Degrees and Radians >
      • 13.1.1. Degrees, Minutes and Seconds
      • 13.1.2. Bradis Table
    • 13.2. Trigonometric Function Keys
    • 13.3. Trigonometric Values of Special Angles >
      • 13.3.1. The 45- 45 - 90 Triangle
      • 13.3.2. The 30-60-90 Triangle
      • 13.3.3. Quadrantal Angles
      • 13.3.4. Coterminal Angles
    • 13.4. Trigonometric Values of 15 Degrees and Its Multiples
    • 13.5. Hyperbolic Function Keys
    • 13.6. Graphing Trigonometric Functions
    • 13.7. Graphing Hyperbolic Functions
    • 13.8. Graphing Inverse Functions
  • 14. Analytic Geometry
    • 14.1. Conic Sections
    • 14.2. Parametric Equations
    • 14.3. Polar Graphs >
      • 14.3.1. Limacon
      • 14.3.2. Cardioid
      • 14.3.3. Lemniscate
      • 14.3.4. Rose
      • 14.3.5. Other Polar Graphs
    • 14.4. 3D Graphing
  • 15. Limits
    • 15.1. Right - hand Limit
    • 15.2. Left - hand Limit
    • 15.3. Limit of a Function
    • 15.4. Limit of a Polynomial Function
    • 15.5. Limit of a Rational Function
    • 15.6. Limit of a Radical Function
    • 15.7. Limit of an Absolute Value Function
    • 15.8. Limit of a Trigonometric Function
    • 15.9. Limit of an Exponential and Logarithmic Function
    • 15.10. Limit of a Piece-wise Function
    • 15.11. Limits at Infinity
    • 15.12. Indeterminate Forms
    • 15.13. Limit of a Hyperbolic Function
  • 16. Derivatives
    • 16.1. First Derivative Key
    • 16.2. Second Derivative Key
    • 16.3. Third and Higher Derivative Keys
    • 16.4. Rules of Differentiation
    • 16.5. Derivatives of Polynomial Functions
    • 16.6. Derivatives of Rational Functions
    • 16.7. Dervatives of Trigonometric, Logarithmic and and Exponential Functions
    • 16.8. More on Derivatives
  • 17. Partial Derivatives
    • 17.1. Increments
    • 17.2. Dervative of a Function df (or dy))
    • 17.3. Derivative of a Function df (f not in terms of x)
    • 17.4. Other Partial Derivatives
    • 17.5. Higher Order Partial Derivatives
    • 17.6. Total Derivates
  • 18. Definite Integral
    • 18.1. Definite Integral of Algebraic Functions
    • 18.2. Definite Integral of Trigonometric Functions
  • 19. Basic Statistics
    • 19.1. Summation Notation
    • 19.2. Product Notation
    • 19.3. Minimum and Maximum
    • 19.4. Factorial, nCr and nPr
    • 19.5. Measures of Central Tendency >
      • 19.5.1. Mean from Ungrouped Data Set
      • 19.5.2. Mean from Frequency Distribution Table
      • 19.5.3. Median from Ungrouped Data Set
      • 19.5.4. Mode
    • 19.6. Measures of Variability >
      • 19.6.1. Range
      • 19.6.2. Interquartile Range and Quartile Deviation
      • 19.6.3. Mean Absolute Deviation
      • 19.6.4. Variance and Standard Deviation
      • 19.6.5. Coefficient of Variation
    • 19.7. Measures of Position
    • 19.8. Bivariate Data Analysis >
      • 19.8.1 Covariance
      • 19.8.2. Correlation Coefficient
      • 19.8.3. Scatter Plot and Regression Line
  • 20. Special Functions
    • 20.1. Gamma Function
    • 20.2. Logarithmic Gamma Function
    • 20.3. Digamma Function
  • 21. List of ALL Functions
    • 21.1. Arithmetics
    • 21.2. Algebra
    • 21.3. Trigonometry
    • 21.4. Statistics
    • 21.5. Calculus

12.1 Matrix Operations

Enter each matrix using brackets. Select open brackets by tapping the open parentheses key twice and select closed brackets by tapping the closed parentheses key twice. Separate data entries using a space and rows of elements using another set of brackets.
Addition and Subtraction
Matrices must have the same corresponding number of rows and columns for addition and subtraction. Missing elements will be replaced with zeros.

Examples
Picture
Calculator solution
Note: tap ( or ) twice to use brackets [ or ].
1) Enter: [[2    3][5    -2]] + [[-1    6][7    -3]]

Picture
Picture
Calculator solution
Note: tap ( or ) twice to use brackets [ or ].​
2) Enter: 2[[2   3][5   -2]] - [[-1   6][7   -3]]
Picture
Multiplication
Note that if you want to multiply two matrices with dimensions k (rows) by l (columns) and m (rows) by n (columns), the resulting matrix will always have dimensions k (rows) by n (columns). If l > m, extra rows or columns will be ignored because the number of columns in the first matrix must equal the number of rows in the second.

Examples
Picture
Calculator solution
Note: tap ( or ) twice to use brackets [ or ].
3) Enter: [[2   3   4][5   -2   -8]] × [[-1   6][7   -3][6   4]]
Picture
Picture
Calculator solution
Note: tap ( or ) twice to use brackets [ or ].
​Enter ^T by tapping the absolute value key |x| six times or by selecting it from the function's drop-down menu.
4) Enter: [[2   3   4][5   -2   -8]]^T × [[-1   6][7   -3][6   4]]
Picture
Matrix Powers
Matrices can be raised to positive integer powers. The result is the same as multiplying the matrix by itself (n-1) times.

Inverse Matrices
To find the inverse matrix, raise the original matrix to a power of -1. You can only do this with square matrices that have a non-zero determinant. Note that division between two matrices is defined as multiplying the numerator by the inverse matrix of the denominator, e.g. A/B = A*(B^-1).

Example
Calculator solution
Note: tap ( or ) twice to use brackets [ or ].
Use the exponent key x^n to enter the exponents.
5) Enter: 2[[2   3][5   -2]]^2 - [[-1   6][7   -3]]^-1​
Picture
Vector Cross and Dot Product
To find a vector cross product, the vectors must have three elements. Vectors with fewer than three elements will be extended with zeros. Use the × multiplication sign to find the cross product between two vectors.

To find a dot or scalar product, use the dot multiplication sign by tapping the multiplication sign twice. The dot also works when multiplying scalars.

Examples
1. Find the cross product of [1, 2, 3] and [4, 5, 6]
2. Find the dot product of [1, 2, 3] and [4, 5, 6]

Calculator solutions
Note: tap ( or ) twice to use brackets [ or ].
1) Enter: [1   2   3] × [4   5   6]
2) Enter: [1   2   3] 
∙ [4   5   6]. Enter the dot product by tapping the multiplication key ( × ) twice.

Picture
NEXT: 12.2. Editing Matrix ENtries>
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