High School
SAT
ACT
University
MCAT
LSAT
DAT

Practice Question: Matrix of an ERO

Related Topics

Wize University Linear Algebra Textbook > Matrices

Elementary Matrices

5 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Let EE be the elementary matrix obtained from I2I_2 by multiplying R2 by 1/3. Let BB be any 2×22\times2 matrix. Show that EBEB is the result of multiplying R2 of BB by 1/3. Find the inverse of EE and show that it is an elementary matrix.
More Elementary Matrices Questions:
Write down matrix A−1A^{-1} as the product of elementary matrices if:
A=[01211021−1]A=\begin{bmatrix}0&1&2\\1&1&0\\2&1&-1\end{bmatrix}
Write down matrix A−1A^{-1} as the product of elementary matrices if:
A=[01211021−1]A=\begin{bmatrix}0&1&2\\1&1&0\\2&1&-1\end{bmatrix}
Elementary matrices
Which of the following are elementary matrices?
A=[10001000−3]B=[0001001001001000]A = \begin{bmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -3\end{bmatrix} \quad B = \begin{bmatrix} 0 & 0 & 0 & 1\\0 & 0 & 1 & 0\\0 & 1 & 0 & 0\\1 & 0 & 0 & 0\end{bmatrix}
C=[001010100]D=[10−71]C = \begin{bmatrix} 0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix} \quad D = \begin{bmatrix} 1 & 0 \\-7 & 1 \end{bmatrix}
Example: Elementary Matrix
Find an elementary matrix EE such that A=EBA=EB if:
A=[246−1−1−11−13]A=\left[\begin{array}{rrr} 2&4&6\\ -1&-1&-1\\ 1&-1&3 \end{array}\right] and B=[246−1−1−1315]B=\left[\begin{array}{rrr} 2&4&6\\ -1&-1&-1\\ 3&1&5 \end{array}\right]
Which of the following are elementary matrices?
A=[10001000−3]B=[0001001001001000]A = \begin{bmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & -3\end{bmatrix} \quad B = \begin{bmatrix} 0 & 0 & 0 & 1\\0 & 0 & 1 & 0\\0 & 1 & 0 & 0\\1 & 0 & 0 & 0\end{bmatrix}
C=[001010100]D=[10−71]C = \begin{bmatrix} 0 & 0 & 1\\0 & 1 & 0\\1 & 0 & 0\end{bmatrix} \quad D = \begin{bmatrix} 1 & 0 \\-7 & 1 \end{bmatrix}
Matrix Multiplication
Express the following matrix A‾\bcb{ \A } as a product of five (or fewer) elementary matrices); repeat for A‾−1\bcb{ \minv{\A} }.
A‾=[−300201010]\bcb{ \A=\begin{bmatrix} -3&0&0\\2&0&1\\0&1&0 \end{bmatrix} }
Practice: Elementary Matrix
Find an elementary matrix EE such that EB=CEB=C if:
B=[11300364]B=\left[\begin{array}{rr} 1&1\\ 3&0\\ 0&3\\ 6&4 \end{array}\right] and C=[101300364]C=\left[\begin{array}{rr} 10&1\\ 3&0\\ 0&3\\ 6&4 \end{array}\right]
Matrix Multiplication
e.g. Express the following matrix A‾\underline{A} as a product of five (or fewer) elementary matrices); repeat for  ⁣A‾−1 ⁣\!\underline{A}^{−1}\!,