Chapter 8: Problem 62
What is a cryptogram?
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
Learning Materials
Features
Discover
Chapter 8: Problem 62
What is a cryptogram?
These are the key concepts you need to understand to accurately answer the question.
All the tools & learning materials you need for study success - in one app.
Get started for free
Use the fact that if \(A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right],\) then \(A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{rr}d & -b \\ -c & a\end{array}\right]\) to find the inverse of each matrix, if possible. Check that \(A A^{-1}=I_{2}\) and \(A^{-1} A=I_{2}\) $$A=\left[\begin{array}{ll} 2 & -6 \\ 1 & -2 \end{array}\right]$$
The figure shows the letter \(L\) in a rectangular coordinate system. GRAPH CAN'T COPY. The figure can be represented by the matrix $$B=\left[\begin{array}{llllll}0 & 3 & 3 & 1 & 1 & 0 \\\0 & 0 & 1 & 1 & 5 & 5\end{array}\right]$$ Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The \(L\) is completed by connecting the last point in the matrix, \((0,5),\) to the starting point, \((0,0) .\) Use these ideas to solve Exercises \(53-60\) Use matrix operations to move the L 2 units to the left and 3 units down. Then graph the letter and its transformation in a rectangular coordinate system.
Write each matrix equation as a system of linear equations without matrices. $$\left[\begin{array}{rrr}2 & 0 & -1 \\\0 & 3 & 0 \\\1 & 1 & 0 \end{array}\right]\left[\begin{array}{l}x \\\y \\\z\end{array}\right]=\left[\begin{array}{l} 6 \\\9 \\\5\end{array}\right]$$
If you are given two matrices, \(A\) and \(B,\) explain how to determine if \(B\) is the multiplicative inverse of \(A\).
Find \(A^{-1}\) by forming \([A | I]\) and then using row operations to obtain \([I | B],\) where \(A^{-1}=[B] .\) Check that \(A A^{-1}=I\) and \(A^{-1} A=I\) $$A=\left[\begin{array}{rrr} 1 & -1 & 1 \\ 0 & 2 & -1 \\ 2 & 3 & 0 \end{array}\right]$$
What do you think about this solution?
We value your feedback to improve our textbook solutions.