Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6

Massachusetts Institute of Technology
Instructor and Grader

Biography

I was an instructor at Kumon for 2 years while in high school, and I taught math and English to children in grades up to high school. I was also an AP Peer Tutor at my high school during my senior year.

Education

BS Computer Science and Molecular Biology & Brain and Cognitive Science
Massachusetts Institute of Technology

Educator Statistics

Numerade tutor for 5 years
45 Students Helped

Topics Covered

Exploring the World of Derivatives: A Comprehensive Guide
Solving Systems of Equations and Inequalities: A Comprehensive Guide
Mastering Matrices: An Introduction to the Fundamentals

bcrypt_sha256$$2b$12$jYG5XsmD/D90HrerlbRJb.VVn1EEC8hpzl08IvucuCkdN8IGliWH6's Textbook Answer Videos

02:14
Student's Solutions Manual for College Algebra

Provide a proof for each of the following.
Show that $I_{3} A=A$ for $A=\left[\begin{array}{rrr}-2 & 4 & 0 \\ 3 & 5 & 9 \\ 0 & 8 & -6\end{array}\right]$ and $I_{3}=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$ (This result, along with that of Example 1 , illustrates that the commutative property
holds when one of the matrices is an identity matrix.)

Chapter 5: Systems and Matrices
Section 8: Matrix Inverses
Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6
02:02
Student's Solutions Manual for College Algebra

Provide a proof for each of the following.
Let $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ and $I_{2}=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] .$ Show that $A I_{2}=I_{2} A=A,$ thus proving that $I_{2}$ is
the identity element for matrix multiplication for $2 \times 2$ square matrices.

Chapter 5: Systems and Matrices
Section 8: Matrix Inverses
Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6
09:33
Student's Solutions Manual for College Algebra

Find the inverse, if it exists, for each matrix.
$\left[\begin{array}{rrrr}1 & -2 & 3 & 0 \\ 0 & 1 & -1 & 1 \\ -2 & 2 & -2 & 4 \\ 0 & 2 & -3 & 1\end{array}\right]$

Chapter 5: Systems and Matrices
Section 8: Matrix Inverses
Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6
16:43
Student's Solutions Manual for College Algebra

Find the inverse, if it exists, for each matrix.
$\left[\begin{array}{rrrr}3 & 2 & 0 & -1 \\ 2 & 0 & 1 & 2 \\ 1 & 2 & -1 & 0 \\ 2 & -1 & 1 & 1\end{array}\right]$

Chapter 5: Systems and Matrices
Section 8: Matrix Inverses
Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6
05:12
Student's Solutions Manual for College Algebra

Solve each system using the inverse of the coefficient matrix.
$$\frac{1}{5} x+\frac{1}{7} y=\frac{12}{5}$$
$$\frac{1}{10} x+\frac{1}{3} y=\frac{5}{6}$$

Chapter 5: Systems and Matrices
Section 8: Matrix Inverses
Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Vvn1Eec8Hpzl08Ivucuckdn8Igliwh6 Bcrypt_Sha256$$2B$12$Jyg5Xsmd/D90Hrerlbrjb.Yfcjxtp7V4Zxsmgv8Xpg.Vn.Fy6Khx6
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