Matrix Algebra Word Scramble
|
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Question | Answer |
What are the possible solutions for a system of n equations in m variables? | 3 - * Unique Solution * No Solution * Infinetly Many Solutions |
What is an example of an unique solution? | ax+by=c dx+ey=f |
What is an example of no solution? | ax+by=c ax+by=d |
What is an example of Infinetly Many Solutions? | ax+by=c k(ax+by=c) |
What is pivoting? | Multiplying a row by a number to get rid of a column. |
Matrix Notation | A matrix is a rectangular array of Real numbers represented as a "nxm matrix" which consists of n rows, each of which contains m entries. Likewise, it consists of m columns each of which has n entries. |
What are the three properties of echelon form? | 1) All nonzero rows are above any rows of all zeros. 2) Each leading entry of a row is in a column to the right of the leading entry of the row above it. 3) All entries in a column below a leading entry are zeros. |
What are the conditions of a rectangular matrix in Reduced Row Echelon Form (RREF) | It must meet the 3 properties of echelon form as well as: 4) the leading entry in each nonzero row is 1. 5) Each leading 1 is the only nonzero entry in its column. |
Are row operations reversible? If yes how, if no, why not? | Yes (i) ri<->rj is "reversed" by rj<->ri (ii) kri->ri is "reversed" by 1/kri->ri (k=0 is not allowed) (iii) kri+rj->rj is "reversed" by -kri+rj-)rj |
R.E.F. | |#****| |0#***| |00#**| |000#*| |
R.R.E.F. | |100*0| |010*0| |001*0| |00001| |
Theorem 1 | Any matrix has 1 and only 1 R.R.E.F. |
Theorem 2 | Any system of linear equations has a unique solution, has infinetly many solutions or else has no solutions. |
Correspondence Theorem | The vector b is in the span {a1, a2,...,an} precisely when the linear system with augmented matrix (a1:a2:...:an|b) has a solution. ie: b=&1a1+&2a2+...+&nan precisely when x1=&1, x2=&2,...,xn=&n is a solution to the linear system. |
What is the matrix equation: |1 2| |x| |7| |3 4|*|y|=|8| |5 6| |9| | x+2y=7 3x+4y=8 5x+6y=9 |
When is column vector defined? | The matrix product Ax where x is an nx1 matrix, column vector is defined only when A is mxn |
Created by:
jibjr
Popular Math sets