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Understanding Matrix Operations: Dimensions, Addition, Subtraction, and Scalar Multiplication

This lesson focuses on key concepts of matrix operations, including dimensions, addition, subtraction, and scalar multiplication. We will explore how only matrices with the same dimensions can be added or subtracted, resulting in a matrix with the same dimensions. Additionally, we will discuss scalar multiplication, where each element of the matrix is multiplied by a constant. Examples will illustrate these concepts, and we'll also tackle some more complex problems involving variable manipulation. Homework includes a worksheet with problems 1-13.

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Understanding Matrix Operations: Dimensions, Addition, Subtraction, and Scalar Multiplication

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  1. Warm-up Review notes from Friday. What is the dimension of the matrix below?

  2. Adding, Subtracting, and Scalar Multiplication of Matrices

  3. Only matrices with the same dimensions can be added and subtracted. • The resulting matrix has the same dimension of the two matrices being added or subtracted.

  4. Add the corresponding elements in each matrix Examples

  5. We can’t add because they are different dimensions!!!

  6. Scalar Multiplication: each element in a matrix is multiplied by a constant.

  7. Examples.

  8. More solving for a variable: A little more complex…

  9. Upon first glance, these do not look equal. But if we manipulate them, we can see they are equal.

  10. What pattern do you see? What can we do to get 5 to equal 25? How about 4 to equal 16?

  11. Homework. Worksheet, problems 1-13.

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