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Questions and Answers
What defines the order of a matrix?
What defines the order of a matrix?
Matrix addition is commutative.
Matrix addition is commutative.
True
What is the identity matrix for a 3 by 3 matrix?
What is the identity matrix for a 3 by 3 matrix?
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
In matrix addition, the resulting matrix C is defined as cij = aij + bij, where A and B have the same dimension. This can only be performed if A and B are of a ____ dimension.
In matrix addition, the resulting matrix C is defined as cij = aij + bij, where A and B have the same dimension. This can only be performed if A and B are of a ____ dimension.
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What is the result of the matrix multiplication AB where A = [[2, -1], [-1, 0], [2, 1]] and B = [[3, -2], [1, -4]]?
What is the result of the matrix multiplication AB where A = [[2, -1], [-1, 0], [2, 1]] and B = [[3, -2], [1, -4]]?
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Matrix multiplication is commutative.
Matrix multiplication is commutative.
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What is the value of AB if A = [[1, 4], [-2, 5]] and B = [[1], [5]]?
What is the value of AB if A = [[1, 4], [-2, 5]] and B = [[1], [5]]?
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In order for two matrices to be multiplied, the number of ___ in the first matrix must equal the number of ___ in the second matrix.
In order for two matrices to be multiplied, the number of ___ in the first matrix must equal the number of ___ in the second matrix.
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Match the matrices to their correct multiplication results:
Match the matrices to their correct multiplication results:
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What is the correct result of the matrix addition A + B if A = [[1, 2, 3], [-2, 1, 4]] and B = [[4, -2], [-2, 4, 4]]?
What is the correct result of the matrix addition A + B if A = [[1, 2, 3], [-2, 1, 4]] and B = [[4, -2], [-2, 4, 4]]?
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Matrix multiplication is possible when the number of columns in the first matrix equals the number of rows in the second matrix.
Matrix multiplication is possible when the number of columns in the first matrix equals the number of rows in the second matrix.
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What do you obtain when you multiply matrix A = [[1, 2, 3], [-2, 1, 4]] by a constant k = 2?
What do you obtain when you multiply matrix A = [[1, 2, 3], [-2, 1, 4]] by a constant k = 2?
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The resulting matrix from multiplying a 2x3 matrix by a 3x4 matrix is a _____ matrix.
The resulting matrix from multiplying a 2x3 matrix by a 3x4 matrix is a _____ matrix.
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What is the result of 2A, if A = [[1, 2, 3], [-2, 1, 4]]?
What is the result of 2A, if A = [[1, 2, 3], [-2, 1, 4]]?
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Match the following operations with their corresponding results:
Match the following operations with their corresponding results:
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What is the result of B - A if A = [[1, 2, 3], [-2, 1, 4]] and B = [[4, -2], [-2, 4, 4]]?
What is the result of B - A if A = [[1, 2, 3], [-2, 1, 4]] and B = [[4, -2], [-2, 4, 4]]?
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B x A can be performed if A is a 2x3 matrix and B is a 3x2 matrix.
B x A can be performed if A is a 2x3 matrix and B is a 3x2 matrix.
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Study Notes
Principles of Mathematics - Chapter 1: Matrices
- Matrices are arrays of numbers with dimensions m (rows) by n (columns)
- A vector can be seen as a 1 x m matrix
- Matrix order, for example, 4 by 3, signifies 4 rows and 3 columns
- Matrix elements are denoted as aij, where i represents the row and j represents the column
- An identity matrix has 1's on the main diagonal and 0's elsewhere; it's used to multiply with any matrix and results in the original matrix
- Matrix addition: Add corresponding elements of two matrices of the same dimension
- Matrix addition is commutative and associative
- Matrix elements must be of the same dimension to add them together
- Matrix multiplication depends on the number of columns in the first matrix and the number of rows in the second matrix
Matrix Operations
- Multiplication by a constant: Multiply all elements of the matrix by the constant
- Matrix multiplication is not commutative (AB ≠ BA)
- Order of matrix multiplication is important
- Only possible to multiply matrices if the number of columns in the first matrix equals the number of rows in the second matrix
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Description
This quiz covers the foundational concepts of matrices, including definitions, operations, and key properties. Learn about matrix dimensions, identity matrices, and the rules for addition and multiplication of matrices. Get ready to test your understanding of this essential mathematical concept!
