4. Verify that the following matrices satisfy the given statements. $A = \begin{bmatrix} 3 & -1 \\ 2 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 0 & 2 \\ 1 & -4 \end{bmatrix}$, $C = \begin{bmatrix} 4 & 1 \\ -3 & -2 \end{bmatrix}$ a) $A(B - C) = AB - AC$ b) $(AB)^T = B^T A^T
Added by Madeline J.
Close
Step 1
To do this, we need to perform the matrix subtraction on the left side of the equation. A - [3 - 1]B = A - [2]B = A - 2B Now, we need to compare this result to the matrix on the right side of the equation, which is [2]. If A - 2B = [2], then the statement is Show more…
Show all steps
Your feedback will help us improve your experience
Khoobchandra Agrawal and 73 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Use $A=\left[\begin{array}{cc}{2} & {-1} \\ {3} & {5}\end{array}\right], B=\left[\begin{array}{cc}{-4} & {1} \\ {8} & {0}\end{array}\right]$ and $C=\left[\begin{array}{cc}{3} & {2} \\ {-1} & {2}\end{array}\right]$ to determine whether the following equations are true for the given matrices. $A B=B A$
Matrices
Multiplying Matrices
Use $A=\left[\begin{array}{cc}{2} & {-1} \\ {3} & {5}\end{array}\right], B=\left[\begin{array}{cc}{-4} & {1} \\ {8} & {0}\end{array}\right]$ and $C=\left[\begin{array}{cc}{3} & {2} \\ {-1} & {2}\end{array}\right]$ to determine whether the following equations are true for the given matrices. $A(B C)=(A B) C$
Use $A=\left[\begin{array}{cc}{1} & {-2} \\ {4} & {3}\end{array}\right], B=\left[\begin{array}{cc}{-5} & {2} \\ {4} & {3}\end{array}\right], C=\left[\begin{array}{cc}{5} & {1} \\ {2} & {-4}\end{array}\right]$ and scalar $c=3$ to determine whether the following equations are true for the given matrices. $c(A B)=A(c B)$
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD