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Questions and Answers
What is the correct order of matrices A, B, and C?
What is the correct order of matrices A, B, and C?
- A is [2×2], B is [3×3], C is [2×3]
- A is [1×2], B is [2×3], C is [3×2]
- A is [2×1], B is [3×2], C is [3×2]
- A is [2×1], B is [3×2], C is [2×3] (correct)
What is the value of d12 in matrix D?
What is the value of d12 in matrix D?
- 5 (correct)
- 2
- 6
- 8
What is the result of E + F?
What is the result of E + F?
- [1 5; 8 6]
- [2 4; 9 7]
- [2 5; 8 7]
- [3 4; 8 6] (correct)
What is the value of 2E - 4F's first element?
What is the value of 2E - 4F's first element?
What is the correct relationship for the values of x and y given matrix H?
What is the correct relationship for the values of x and y given matrix H?
Which of the following matrices has a dimension of [2×2]?
Which of the following matrices has a dimension of [2×2]?
What is the value of d23 as per matrix D?
What is the value of d23 as per matrix D?
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?
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?
What is the vector $\overrightarrow{\text{AB}}$ for points A(3,4) and B(-2,5)?
What is the vector $\overrightarrow{\text{AB}}$ for points A(3,4) and B(-2,5)?
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)?
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)?
What is the magnitude of the vector $\overrightarrow{\text{DE}}$ for points D(-3,8) and E(5,-6)?
What is the magnitude of the vector $\overrightarrow{\text{DE}}$ for points D(-3,8) and E(5,-6)?
What is the correct order of matrix A $[2 \ 4]$?
What is the correct order of matrix A $[2 \ 4]$?
What is the order of matrix C $\begin{bmatrix} 4 & 6 & 3 \newline 1 & 2 & 1 \end{bmatrix}$?
What is the order of matrix C $\begin{bmatrix} 4 & 6 & 3 \newline 1 & 2 & 1 \end{bmatrix}$?
If the vector $\overrightarrow{\text{AB}}$ points from A(2,3) to B(5,7), what is the vector representation?
If the vector $\overrightarrow{\text{AB}}$ points from A(2,3) to B(5,7), what is the vector representation?
Which of the following statements is true about the vector $\overrightarrow{\text{OC}}$ derived from $3\overrightarrow{\text{OA}} = \overrightarrow{\text{OB}} - 6\overrightarrow{\text{OC}}$?
Which of the following statements is true about the vector $\overrightarrow{\text{OC}}$ derived from $3\overrightarrow{\text{OA}} = \overrightarrow{\text{OB}} - 6\overrightarrow{\text{OC}}$?
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Study Notes
Vectors
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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
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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)
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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
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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})
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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.
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