Equality of Matrices Two matrices are said to be equal if they have the same size and their corresponding entries are equal
Equality of Matrices Use the given equality to find x, y and z
Matrix Multiplication(n by m) Matrix X (m by k) MatrixThe number of columns of the matrix on the left= number of rows of the matrix on the right The result is a (n by k) Matrix
Matrix ReductionDefinitions (1) 1. Zero Row:A row consisting entirely of zeros 2. Nonzero Row:A row having at least one nonzero entry 3. Leading Entry of a row:The first nonzero entry of a row.
Matrix ReductionDefinitions (2) Reduced Matrix: A matrix satisfying the following: 1. All zero rows, if any, are at the bottom of the matrix 2. The leading entry of a row is 1 3. All other entries in the column in which the leading entry is located are zeros. 4. A leading entry in a row is to the right of a leading entry in any row above it.
Elementary Row Operations 1. Interchanging two rows 2. Replacing a row by a nonzero multiple of itself 3. Replacing a row by the sum of that row and a nonzero multiple of another row.
Replacing a row by the sum of that row and a nonzero multiple of another row
Solving a System of Linear Equations by Reducing its Augmented Matrix Using Row Operations
Subtracting from the Third Equation 5 times the First Equation
Subtracting from the First Equation 2 times the Second Equation
Subtracting from the Second Equation 3/2 times the third Equation