Mathematics
Grade 11
15 min
Add and subtract scalar multiples of matrices
Add and subtract scalar multiples of matrices
What you'll learn
- Solve word problems to find two unknown numbers when given their sum and difference, achieving at least 80% accuracy on a worksheet with 5 problems.
- Explain in their own words, using at least two sentences, how to use addition and subtraction to find two numbers when you know their sum and difference.
- Apply the learned strategy to create their own word problem involving the sum and difference of two numbers, and correctly solve it.
- Identify the sum and the difference from a word problem with 100% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a scalar and perform scalar multiplication on a matrix of any dimension.
Determine if two matrices can be added or subtracted based on their dimensions.
Accurately add two or more matrices of the same dimensions.
Accurately subtract one matrix from another of the same dimensions.
Evaluate complex expressions involving a combination of scalar multiplication, matrix addition, and matrix subtraction.
Solve for an unknown matrix in a linear equation involving scalar multiples and matrix addition/subtraction.
Ever wondered how a photo editor can uniformly increase the brightness of an entire image with one slider? 🖼️ That's a real-world application of multiplying a matrix (the image pixels) by a scalar!
This tutorial will guide you through the fun...
2
Key Concepts & Vocabulary
TermDefinitionExample
MatrixA rectangular array of numbers, symbols, or expressions, arranged in rows and columns. It is typically enclosed in square brackets.A = \begin{bmatrix} 2 & -1 \\ 0 & 5 \end{bmatrix} is a 2x2 matrix.
ScalarAn ordinary number (a real number) that is used to multiply a matrix. It 'scales' the matrix up or down.In the expression 3A, the number 3 is a scalar.
Dimensions of a MatrixThe size of a matrix, described by its number of rows and columns. It is written as 'rows x columns'.The matrix \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} has dimensions 2x3.
Scalar MultiplicationThe operation of multiplying a matrix by a scalar. Every element inside the matrix is multiplied by the scalar.If k=4 and A = \begin{bmatrix} 1...
3
Core Formulas
Scalar Multiplication Rule
If k is a scalar and A = [a_{ij}], then kA = [k \cdot a_{ij}]
To multiply a matrix by a scalar, you must multiply every single element within the matrix by that scalar. The dimensions of the resulting matrix are the same as the original matrix.
Matrix Addition Rule
If A = [a_{ij}] and B = [b_{ij}], then A + B = [a_{ij} + b_{ij}]
To add two matrices, they MUST have the exact same dimensions. The resulting matrix is found by adding the elements in the corresponding positions (e.g., row 1, column 1 of A is added to row 1, column 1 of B).
Matrix Subtraction Rule
If A = [a_{ij}] and B = [b_{ij}], then A - B = [a_{ij} - b_{ij}]
To subtract two matrices, they MUST have the exact same dimensions. The resulting matrix is found by subtracting the ele...
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Easy
In the context of matrix operations, what is the definition of a 'scalar'?
A.matrix with only one row.
B.The dimensions of a matrix.
C.An ordinary number used to multiply a matrix.
D.The element in the first row and first column of a matrix.
Easy
Under which condition can two matrices, A and B, be added together to find A + B?
A.The number of columns in A must equal the number of rows in B.
B.They must have the exact same dimensions.
C.They must both be square matrices.
D.The number of rows in A must equal the number of columns in B.
Easy
Given the matrix A = \begin{bmatrix} 5 & -1 \ 0 & 3 \end{bmatrix}, what is the result of the scalar multiplication 4A?
A.\begin{bmatrix} 20 & -4 \ 0 & 12 \end{bmatrix}
B.\begin{bmatrix} 9 & 3 \ 4 & 7 \end{bmatrix}
C.\begin{bmatrix} 20 & -1 \ 0 & 3 \end{bmatrix}
D.\begin{bmatrix} 20 & -4 \ 0 & 3 \end{bmatrix}
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Add and subtract scalar multiples of matrices is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Add and subtract scalar multiples of matrices?
You'll be able to: Solve word problems to find two unknown numbers when given their sum and difference, achieving at least 80% accuracy on a worksheet with 5 problems; Explain in their own words, using at least two sentences, how to use addition….
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This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.