IB DP Maths: AI HL复习笔记1.7.2 Operations with Matrices
Matrix Addition & Subtraction
Just as with ordinary numbers, matrices can be added together and subtracted from one another, provided that they meet certain conditions.
How is addition and subtraction performed with matrices?
- Two matrices of the same order can be added or subtracted
The resultant matrix is of the same order as the original matrices being added or subtracted
What are the properties of matrix addition and subtraction?
Exam Tip
- Make sure that you know how to add and subtract matrices on your GDC for speed or for checking work in an exam!
Worked Example
Matrix Multiplication
Matrices can also be multiplied either by a scalar or by another matrix.
How do I multiply a matrix by a scalar?
- Multiply each element in the matrix by the scalar value
The resultant matrix is of the same order as the original matrix- Multiplication by a negative scalar changes the sign of each element in the matrix
How do I multiply a matrix by another matrix?
- To multiply a matrix by another matrix, the number of columns in the first matrix must be equal to the number of rows in the second matrix
How do I square an expression involving matrices?
- remember, the regular rules of algebra do not apply here and you cannot expand these brackets, instead, add together the matrices inside the brackets and then multiply the matrices together
What are the properties of matrix multiplication?
Exam Tip
- Make sure that you are clear on the properties of matrix algebra and show each step of your calculations
Worked Example
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