### Figure ABCD is a Trapezoid with point A (0, −4). What rule would rotate the figure 270° clockwise?

This question aims to find the type of rule that would be applied to the trapezoid ABCD with a point A( 0, -4 ) to rotate it to 270° in the clockwise direction. A quadrilateral having two sides parallel to each other is called a trapezoid. This four-sided figure is also called a trapezium. When […]

### A and B are n x n matrices. Mark each statement True or False. Justify your answer.

A row replacement operation does not affect the determinant of a matrix. The determinant of $A$ is the product of the pivots in any echelon form $U$ of $A$, multiplied by $(-1)^r$, where $r$ is the number of row interchanges made during row reduction from $A$ to $U$. If the columns of $A$ are linearly […]

### For the matrix, list the real eigenvalues, repeated according to their multiplicities.

[ begin{bmatrix} 4 & -5 & 7 & 0 \ 0 & 3 & 1 & -5 \ 0 & 0 & 1 & 2 \ 0 & 0 & 0 & 1 end{bmatrix} ] This question aims to find the eigenvalues of an upper triangular matrix which are repeated according to their multiplicities. The […]

### Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.

[ boldsymbol{ left[ begin{array}{ c c | c } 1 & 3 & -8 \ -4 & h & 1 end{array} right] } ] The aim of this question is to understand the solution of the system of linear equations using the row operations and row echelon form. Any matrix is said to be in […]

### Find the value(s) of h for which the vectors are linearly dependent. Justify your answer.

The main objective of this question is to determine which of the following vectors are linearly dependent. This question uses the concept of linearly dependent. If the non-trivial linear combination of vectors is equal to zero, then that set of vectors is said to be linearly dependent while the vectors are said to be linearly […]