Questions and Answers
What is the correct order of matrices A, B, and C?
What is the value of d12 in matrix D?
What is the result of E + F?
What is the value of 2E - 4F's first element?
Signup and view all the answers
What is the correct relationship for the values of x and y given matrix H?
Signup and view all the answers
Which of the following matrices has a dimension of [2×2]?
Signup and view all the answers
What is the value of d23 as per matrix D?
Signup and view all the answers
If the first element of E is multiplied by 2 and then F's first element is multiplied by -4, what is the resulting first element in 2E - 4F?
Signup and view all the answers
What is the vector $\overrightarrow{\text{AB}}$ for points A(3,4) and B(-2,5)?
Signup and view all the answers
Given the equation $3\overrightarrow{\text{OA}} = \overrightarrow{\text{OB}} - 6\overrightarrow{\text{OC}}$, what is $\overrightarrow{\text{OC}}$ if A(6,2) and B(-4,3)?
Signup and view all the answers
What is the magnitude of the vector $\overrightarrow{\text{DE}}$ for points D(-3,8) and E(5,-6)?
Signup and view all the answers
What is the correct order of matrix A $[2 \ 4]$?
Signup and view all the answers
What is the order of matrix C $\begin{bmatrix} 4 & 6 & 3 \newline 1 & 2 & 1 \end{bmatrix}$?
Signup and view all the answers
If the vector $\overrightarrow{\text{AB}}$ points from A(2,3) to B(5,7), what is the vector representation?
Signup and view all the answers
Which of the following statements is true about the vector $\overrightarrow{\text{OC}}$ derived from $3\overrightarrow{\text{OA}} = \overrightarrow{\text{OB}} - 6\overrightarrow{\text{OC}}$?
Signup and view all the answers
Study Notes
Vectors
-
Vector from Point A to B: For points A(3,4) and B(-2,5), the vector (\overrightarrow{AB}) can be calculated as:
- (\overrightarrow{AB} = B - A = (-2 - 3)i + (5 - 4)j = -5i + j)
-
Finding (\overrightarrow{OC}): Given the relationship (3\overrightarrow{OA} = \overrightarrow{OB} - 6\overrightarrow{OC}) for points A(6,2) and B(-4,3), solving for (\overrightarrow{OC}) yields:
- (\overrightarrow{OC} = -\frac{11}{3}i - \frac{1}{2}j)
-
Magnitude of (\overrightarrow{DE}): For points D(-3,8) and E(5,-6), the magnitude can be calculated using the distance formula:
- (\left| \overrightarrow{DE} \right| = \sqrt{(5 - (-3))^2 + (-6 - 8)^2} = \sqrt{8^2 + (-14)^2} = 3\sqrt{281})
Matrices
-
Order of Matrices: For matrices:
- (A = \begin{bmatrix} 2 & 4 \end{bmatrix}) has an order of (1 \times 2)
- (B = \begin{bmatrix} 8 \ 5 \ 2 \end{bmatrix}) has an order of (3 \times 1)
- (C = \begin{bmatrix} 4 & 6 & 3 \ 1 & 2 & 1 \end{bmatrix}) has an order of (2 \times 3)
-
Identifying Matrix Elements: For matrix (D = \begin{bmatrix} 2 & 6 & 9 \ 1 & 5 & 8 \ 3 & 4 & 7 \end{bmatrix}):
- Element d~12 = 5
- Element d~23 = 8
- Element d~31 = 3
-
Matrix Addition: For matrices (E = \begin{bmatrix} 2 & 8 \ 3 & 7 \end{bmatrix}) and (F = \begin{bmatrix} 1 & 4 \ 5 & -1 \end{bmatrix}):
- The sum (E + F = \begin{bmatrix} 3 & 12 \ 8 & 6 \end{bmatrix})
-
Matrix Operations: For the operation (2E - 4F):
- Calculating gives (2E = \begin{bmatrix} 4 & 16 \ 6 & 14 \end{bmatrix})
- Calculating (4F = \begin{bmatrix} 4 & 16 \ 20 & -4 \end{bmatrix})
- Therefore, (2E - 4F = \begin{bmatrix} 1 & 4 \ 14 & 11 \end{bmatrix})
-
Finding Variable Values: For matrices (G = \begin{bmatrix} 2 & 8 \ 3 & 7 \end{bmatrix}) and (H = \begin{bmatrix} x + 3 & y - 4 \ 3 & 7 \end{bmatrix}):
- Set equalities from first elements: (2 = x + 3) leads to (x = -1)
- Second elements: (8 = y - 4) leads to (y = 12)
Absolute Value/Inequalities
- The section on absolute values and inequalities is unprovided. Understanding the principles involves recognizing that absolute values represent the distance from zero, while inequalities indicate a range of values.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of vector mathematics with this quiz focused on Cartesian coordinates. Solve problems involving direction and magnitude of vectors between points on a plane. Perfect for students in geometry or physics classes.
