10 Questions
What is the process called when a row in a matrix is replaced by the sum of that row and another row?
Row operation
In a matrix, what is the condition for it to be in row echelon form?
The first non-zero element in each row is the leading entry, and each leading entry is to the right of the leading entry in the previous row.
What is the additional condition for a matrix to be in reduced row echelon form compared to row echelon form?
The leading entry in each row must be 1, and it must be the only non-zero entry in its column.
Define a linear equation in terms of unknowns and constants.
A linear equation in unknowns x, y, z is of the form: ax + by + cz = b, where a, b, c are constants.
What are the coefficients in a linear equation?
The constants a, b, c in the equation ax + by + cz = b are the coefficients of x, y, z.
What is the term used for the constant on the right side of a linear equation?
Constant term
What operation involves changing the order of rows in a matrix?
Interchanging rows
What does a row in a matrix become when it is multiplied by a scalar value?
Scaled
What is the role of the leading entry in each row of a matrix in row echelon form?
It helps determine the structure of the matrix and the position of subsequent leading entries.
What is the key characteristic of the leading entry in each row of a matrix in reduced row echelon form?
The leading entry is always 1.
Test your knowledge on Matrices, Linear Equations, Vector Spaces, Matrix Operations, Rank, Determinants, and more from the syllabus of B.Tech 1st Year, II Sem. Department of Mathematics at SR University.
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