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Questions and Answers
What is a matrix?
What is a matrix?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
How is the order of a matrix defined?
How is the order of a matrix defined?
The order of a matrix is defined by the number of rows and columns, denoted as m × n.
A matrix is said to be a Null (Zero) Matrix if at least one entry of the matrix is non-zero.
A matrix is said to be a Null (Zero) Matrix if at least one entry of the matrix is non-zero.
False (B)
A matrix is a square matrix if the number of rows is equal to the number of columns.
A matrix is a square matrix if the number of rows is equal to the number of columns.
What is a diagonal matrix?
What is a diagonal matrix?
What is an identity matrix?
What is an identity matrix?
What is a scalar matrix?
What is a scalar matrix?
What does the trace of a matrix represent?
What does the trace of a matrix represent?
Matrix addition involves adding corresponding elements of two matrices, A = [a_ij] and B = [b_ij], resulting in C = [____].
Matrix addition involves adding corresponding elements of two matrices, A = [a_ij] and B = [b_ij], resulting in C = [____].
In matrix multiplication, the product A.B exists only if ____ = ____.
In matrix multiplication, the product A.B exists only if ____ = ____.
Compute the product of the matrices A and B, where A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]].
Compute the product of the matrices A and B, where A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]].
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Study Notes
Revision of Matrix
- A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
- The order of a matrix refers to the number of rows and columns.
- If a matrix has m rows and n columns, its order is 𝑚 × 𝑛.
Types of Matrices
- A null (zero) matrix has all entries as zero.
- A square matrix has an equal number of rows and columns.
- A diagonal matrix is a square matrix where all elements outside the main diagonal are zero.
- An identity matrix is a special type of square matrix with diagonal elements as 1 and off-diagonal elements as 0.
- A scalar matrix is a square matrix where all elements outside the main diagonal are zero and all diagonal elements are equal.
- The trace of a matrix is the sum of the elements on the main diagonal of a square matrix.
Operations on Matrices
- Matrix addition: 𝐴 + 𝐵 = 𝑎𝑖𝑗 + 𝑏𝑖𝑗 for matrices 𝐴 = 𝑎𝑖𝑗 and 𝐵 = 𝑏𝑖𝑗 of the same order.
- Matrix subtraction: 𝐴 − 𝐵 = 𝑎𝑖𝑗 − 𝑏𝑖𝑗 for matrices 𝐴 = 𝑎𝑖𝑗 and 𝐵 = 𝑏𝑖𝑗 of the same order.
- Matrix multiplication: 𝐴.𝐵 = 𝑗=1 𝑎𝑖𝑗 𝑏𝑗𝑘 for matrices 𝐴 = 𝑎𝑖𝑗 and 𝐵 = 𝑏𝑖𝑗, where the number of columns in 𝐴 equals the number of rows in 𝐵.
- Scalar multiplication: 𝑐𝐴 = 𝑐𝑎𝑖𝑗 for matrix 𝐴 = 𝑎𝑖𝑗 and a scalar c.
- Transpose of a matrix: 𝐴𝑇 = 𝑎𝑖𝑗 for matrix 𝐴 = 𝑎𝑖𝑗.
Activity-1
- Calculate the product of the matrices provided in the activity.
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