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Notes in ES1A8 - Engineering Maths

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ES1A8 - Engineering Maths Flashcards (2024-2025)


    1. Set 1 (Exam: 27-Mar)

    1. - Matrices
    1. - Vectors
    1. - Probability distributions
    1. - Complex numbers

Status Last Update Fields
Published 02/08/2025 Show \(u=2i+3j\) as a column vector
Published 02/08/2025 What do you get when you multiply a vector by a scalare.g.\(u=4i+2j\)\(2u = 8i+4j\)
Published 02/08/2025 How can you find the magnitude (i.e. size/length) of a vectore.g.\(v = \begin{bmatrix} x \\ y \\ z\end{bmatrix}\)
Published 02/08/2025 What is the dot product (or scalar product) of these two vectors\(u = \begin{bmatrix} 3 \\ 5 \end{bmatrix} \ \ \ \ v = \begin{bmatrix} -1 \\ 4 \end{bm…
Published 02/19/2025 If the dot product of two vectors is equal to 0, then the two vectors are {{c1::perpendicular}}
Published 02/08/2025 What happens when you multiply an \(m\times n \) by an \(n\times k \) matrix
Published 02/08/2025 What happens when you multiply a \(n\times m \) matrix by a \(n\times k \) matrix
Published 02/08/2025 Solve:\[\begin{bmatrix} 3 & 2 \\ 5 & 1 \end{bmatrix} \times \begin{bmatrix} 1 & 4 \\ 3 & 6 \end{bmatrix}\]
Published 02/08/2025 A, B & C are three matrices. Is the following true?\[A(BC)=(AB)C\]
Published 02/08/2025 Is the following true when multiplying matrices?\[AB\ne BA\]
Published 02/08/2025 What is the result when a \(n\times n \) matrix is multiplied by \(I_n\) (\(n\times n\) identity matrix)
Published 02/08/2025 What is the determinant of \[\begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}\]
Published 02/11/2025 A matrix with a determinant of 0 has no {{c1::inverse}}
Published 02/08/2025 What is the inverse of \[A=\begin{bmatrix} 2 & 1 \\ 1 & 4 \end{bmatrix}\]\(det(A)=7\)
Published 02/08/2025 Re-write the simultaneous equations as one matrix equation\(7x+5y=3\)\(x+3y=2\)
Published 02/08/2025 How would you solve this matrix equation?\[\begin{bmatrix} 7 & 5 \\ 1 & 3 \end{bmatrix}\times \begin{bmatrix} x \\ y \end{bmatrix} =\begin{bma…
Published 02/12/2025 If both A & B are square matrices (\(n\times n\)) and \(A\cdot B=I_n\)Then what can you assume of A & B
Published 02/19/2025 How would you solve this matrix equation?Find B when \(AB=C\) \[A= \begin{bmatrix} 2 & 1 \\ 4 & -3 \end{bmatrix} \ \ C= \begin{bmatr…
Published 02/11/2025 Identity Matrix have {{c1::all 1's}} in {{c1::leading}} diagonal
Published 02/11/2025 What is the Transpose of a Matrix?
Published 02/11/2025 Transpose this Matrix\(A= \begin{bmatrix} 3 & 6 & 1 \\ 1 & 8 & 9 \end{bmatrix}\)
Published 02/11/2025 How do you find the Determinant of a 3x3 Matrixe.g. \(A = \begin{bmatrix} 3 & 8 & 9 \\ 2 & 4 & 6 \\ 5 & 3 & 8 \end{bmatri…
Published 02/11/2025 What is the Sign Matrix?
Published 02/11/2025 Find the minor of the element \(a_{21}\)
Published 02/11/2025 What is the determinant of a matrix when all elements in a row or column = 0
Published 02/19/2025 What is the determinant of a matrix when two rows or columns are the same. For Example:\(\begin{vmatrix} 2 & 5 & 8 \\ 3 & 7 & 4 \\ 2 &…
Published 02/11/2025 What is the determinant of a matrix when one row (or column) is a multiple of another. For exmple\(A= \begin{bmatrix} 2 & 4 & 6 \\ 3 & 6 &…
Published 02/11/2025 What is the relationship between \(|A|\) & \(|A'|\)\(A= \begin{bmatrix} 2 & 7 & 8 \\ 9 & 3 & 2 \\ 2 & 3 & 8…
Published 02/19/2025 If a matrix is multiplied by a scalar then \(det(\lambda A)=\)
Published 02/12/2025 What is a diagonal matrix?
Published 02/12/2025 What does \(C^Tv\) tell you when solving a Simultaneous Equation Matrix with \(det(A)=0\)\(C^Tv\ne0\) then?\(C^Tv=0\) then?
Published 02/19/2025 Write these simultaneos equations in augmented matrix form\[\begin{cases} 2x + y - z = 8 \\ -3x - y + 2z = -11 \\ -2x + y + 2z = -3 \end{cases}\]
Published 02/12/2025 Gaussian EliminationWhat Row operations can you do to get 0's in bottom corner?
Published 02/19/2025 Write the column vector below in Component Form:\(a=\begin{bmatrix} 1 \\ 4 \\ -3 \end{bmatrix}\)
Published 02/19/2025 Find the magnitude of this vector\[a= 4\hat i+2\hat j+4\hat k\]
Published 02/12/2025 What is a Unit Vector
Published 02/19/2025 What is the dot product (scalar product)
Published 02/19/2025 Find the Dot Product of these matrices\(a= \begin{bmatrix} 2 \\ 6 \\ 8 \end{bmatrix} \quad b= \begin{bmatrix} 3 \\ -2 \\ 4 \end{bmatrix}\)
Published 02/19/2025 How would you find the angle between these two vectors For Example:\(a= \begin{bmatrix} 2 \\ 6 \\ 8 \end{bmatrix} \quad b= \begin{bmatrix} 3 \\ …
Published 02/19/2025 What is the name of this form of a Vector Straight Line Equation\[\mathbf{r} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} + \lambda \begin{pmat…
Published 02/19/2025 Name the parts of this Parametric Line Equation\[ x = a_1 + \lambda\ b_1\]
Published 02/19/2025 What is the name of this form of a Vector Straight Line Equation\[\frac{x - a_1}{b_1} = \frac{y - a_2}{b_2} = \frac{z - a_3}{b_3}\]
Published 02/19/2025 What is the name of this form of a Vector Straight Line Equation & what is B\[ (\mathbf{r} - \mathbf{a}) \times \mathbf{b} = \mathbf{0} \]
Published 02/19/2025 What does the Venn Diagram of the below look like:\[A\cup D\]
Published 02/19/2025 What does the Venn Diagram of the below look like:\[A\cap D\]
Published 02/19/2025 What does the Venn Diagram of the below look like:\[A'\]
Status Last Update Fields

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