8.1: matrix

Row-echelon form (REF): 3 conditions? (3) term for 1? condition 3: In two successive rows without all zeros, the leading one of the higher row is farther to the left than the leading one in the?

If present, any row with all zeros has to be at the bottom/each row has the number 1 for its first nonzero teem/In TWO successive rows without all zeros, the 1 in the higher row is farther to the left, the leading one, lower row

Row Operations: three forms? (3) interchanging row notation? ex. R1 ⟷ R2. What does that mean? ⟷ means to? Multiplying by a constant: ex. -5R1 ⟶R1. what does that mean? Adding a multiple of a row to another row: ex. -2R2 + R3 ⟶ R3. What does that mean? Make sure to apply the row operation to every? (in that?) ex. -2R2 + R3 ⟶ R3. Multiply each R2 value by?-Add to each corresponding? When the z = 1 in R3, you can stop?

interchange two rows/multiply a row by a constant that is not zero/add a multiple of a row to another row, ⟷, the values of R1 replace the values of R2, replace, -5 times row 1 replaces the original row 1 values, -2 times row 2 plus the values of row 3 replace row 3, number in that row, -2, R3 value, reducing

Gauss-Jordan: Solve until there are zeros above each of the? write the solution in a? Bottom with all or three zeros: there is no? 3 variables (x, y, z,) need? If there is no definite solution, substitue variables with? ex. z=a. Solving: Eliminate numbers starting with the first? Gauss-Jordan: it follows which form? 4 conditions? (4)

leading ones (1s), parentheses, solution, 3 equations,constants, row, reduced row echelon form, the first non-zero term is 1/the leading one in the higher row is farther to the left than the 1 in the lower row/an entire row of zeros is the last row/each leading one has zeros above and below it

Row matrix? Column matrix? Equation for notation? ex. [2 5 3} ? If m= n: equation? Notation: Use?

matrix with one row, matrix with one column, # of rows x # of columns, 1 x 3, square of (m x n), brackets

You can also subtract? ex. R1--R2 = R2. To solve for gaussian-elimination: two steps? (2)

rows,get a 1 in the first row and column/eliminate everything beneath it

System with no solution: A row with all zeros has no? Reduced-Row echelon: What is the condition for this? The columns without leading ones can be?

solution, every column with a leading 1 must have zeros above and below it, left alone

Gaussian-Elimination: reduce with row operations until the third variable =? 3 variables? Back substitution: Plug in the? Write the? Two conditions: convert everything below the diagonal of one into? Then convert the last term of the third row into a? The final answer can be a? ALWAYS convert the variable coefficients into? (2)

substitutable number, x/y/z, variables, equations, zeros, one, fraction, 1's/0's,

main diagonal def.? When ordering an augmented matrix: organize according to? ex. x, y, z, and w variables.

the diagonal from the upper left corner to the lower right corner, variables

Calculator Function to Check Matrix: First, 2nd to which function?-Exit to get to the? go to math and press which function?-Plug in the?

x^-1, home screen, (rref, matrix,

4 ways to solve system of equations? (4) Inverse method: equation of system? A is? X? B? First, find the?-equation to find values? Gaussian elimination: if you can turn the last row into all zeros, then...?

Gaussian elimination with back substitution/gaussian-jordan/inverse/cramer's rule, AX=B, coefficient values, variables, solution value matrix, inverse, X = A^-1 x B, do it

Two types of Gaussian? (2)

Gaussian elimination with back-substiution tute and row echelon form/Gaussian-Jordan and reduced row echelon formv

Gaussian elimination and gauss-Jordan: of all the coefficients of the variables are zeros, then there is no? If there is an entire bottom row of zeros, then the last variable (ex. Z) will be a?

Solution, constant

System with infinitely many solutions: What is a defining feature? What do you do?-Use the constant to find the other?

an entire row of zeros, substitute the last variable with constant "a," variables,

Coefficient matrix only has? ex. [5 6 7] Augmented matrix is derived from a system of? Steps to solve? (2) Empty spaces will have a coefficient of? Use the new coefficient table to find the? (of the?) ex. 4x 5 matrix. (You have to write matrix after the order.)

coefficients, linear equations, rearrange the table/write down the coefficients, 0, order of the matrix