5 Questions
Match the following matrix types with their definitions:
Non-singular matrix = Determinant is not equal to 0 Singular matrix = Determinant is equal to 0 Orthogonal matrix = Product of matrix and its transpose gives an identity matrix System of linear equations = Collection of one or more linear equations
Match the following matrices with their determinants:
$\begin{bmatrix} 8 & 1 \ 4 & 2 \end{bmatrix}$ = Determinant = 8 - 8 = 0 $\begin{bmatrix} -3 & 0 & -7 \ 4 & 7 & -4 \end{bmatrix}$ = Determinant ≠ 0 $\begin{bmatrix} -1 & 0 \ 0 & -1 \end{bmatrix}$ = Determinant = 1 $\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$ = Determinant = 1
Match the following linear equations with their representations:
$ax + by = c$ = Representation of a straight line in the $xy$-plane System of linear equations = Collection of one or more equations involving linear terms $3x - 4y = 7$ = Representation of a straight line in the $xy$-plane $2x + 5y = 9$ = Representation of a straight line in the $xy$-plane
Match the following terms with their definitions:
Non-singular matrix = Matrix with a non-zero determinant Singular matrix = Matrix with a zero determinant Orthogonal matrix = Matrix such that the product of the matrix and its transpose gives the identity matrix System of linear equations = Collection of one or more linear equations
Match the following matrices with their transposes:
$\begin{bmatrix} -3 & 0 & -7 \ 4 & 7 & -4 \end{bmatrix}$ = $\begin{bmatrix} -3 & 4 \ 0 & 7 \ -7 & -4 \end{bmatrix}$ $\begin{bmatrix} -1 & 0 \ 0 & -1 \end{bmatrix}$ = $\begin{bmatrix} -1 & 0 \ 0 & -1 \end{bmatrix}$ $\begin{bmatrix} 8 & 1 \ 4 & 2 \end{bmatrix}$ = $\begin{bmatrix} 8 & 4 \ 1 & 2 \end{bmatrix}$ $\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$ = $\begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}$
Test your understanding of matrices with this quiz covering the basics of matrices, their elements, and array representation. This quiz is designed for 1st-year B.Tech students in the Department of Applied Sciences and Humanities at Parul University's Faculty of Engineering & Technology.
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