IB DP Maths: AI HL复习笔记1.7.2 Operations with Matrices

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?

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 matrixHow 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?