# Matrices Worksheets

BYJU’S has made this effort to provide students with a platform where the amount of preparation that they have can be tested, and they can get a clear understanding of the subject what they are dealing with. The tests and examinations that the students go through will not be a big deal when they go through these maths worksheets in a proper environment. As the sheets are topic-based, practising them will give the student a command over the specific topic which will act as a clear indication of growth in a subject. This growth will provide you with the confidence of progress, giving you an edge over others. The worksheets are extremely reliable as they are prepared by trained tutors.

These worksheets are easy to use and free to download as we care about spreading the love for learning. Both theory and exercises are covered in these worksheets so that the students receive a whole round development. A matrix is a group of numeric’s of which every single piece gives a specific piece of information. The various topics discussed under the heading will be the equality of matrices, Order, addition, and subtraction of matrices, multiplication of matrices, Identity and Inverse matrices, an inverse of a 3×3 matrix. The various subheadings that were explored in theory will also have a lot of examples solved, which will give the students solving them an edge in the variety of question they would have seen.

A student’s exam performance is much dependent on what they do in the exam hall. Time is one such factor that is highly based on practice. The speed that they work at in the comfort of their home hugely varies from the speed required to attempt the entire questionnaire in the examination. These worksheets explore all the different types of problems in all the various topics in detail for the benefit of students.

### Worksheet on Matrix Problems

Solve the problems on matrices given below:

 Find the order of the matrix: $\begin{bmatrix} 8 & 1 & 7\\ 9 & 4 & -5 \end{bmatrix}$ Find the sum of the given matrix: $\begin{bmatrix} -10 & 10\\ -17 & -2 \end{bmatrix} +\begin{bmatrix} -11 & -3 \\ -7& -2 \end{bmatrix}$. Subtract the matrices: $\begin{bmatrix} 17 & 4\\ -16 & 11 \end{bmatrix} -\begin{bmatrix} 20 & 16\\ 0& -6 \end{bmatrix}$. Multiply the given matrix by a given scalar: $6\begin{bmatrix} 20 & -12\\ -11 & 9 \end{bmatrix}$. Find the product of the matrices: $\begin{bmatrix} -9\\ 18\\ 10\\ 4 \end{bmatrix}\times \begin{bmatrix} -9 & 5\end{bmatrix}$. Find the value x: $\begin{bmatrix} 13 & -3x & -7 \end{bmatrix} -(\begin{bmatrix} -18 & -19 & 0 \end{bmatrix}+\begin{bmatrix} 2 & 18 & 9 \end{bmatrix})= \begin{bmatrix} 29 & 16 & -16 \end{bmatrix}$. Calculate the inverse of the matrix: $\begin{bmatrix} 7 &4 \\ 12 & -7 \end{bmatrix}$. Write the linear system of equations in the matrix form: -1x-5y=-51 and 9x-2y= -152. Compute the determinant for 2×2 matrix: $\begin{bmatrix} -3 & -19\\ 3 & 13 \end{bmatrix}$ Compute the determinant for 3×3 matrices using the diagonal method: $\begin{bmatrix} -2 & 0 & 17\\ 12 & 10& 8\\ 6& -17 & 15 \end{bmatrix}$ Solve the given matrix equation: $\begin{bmatrix} 5 &-12 \\ 0 & -2 \end{bmatrix}X =\begin{bmatrix} -38 &13 \\ -8 & 8 \end{bmatrix}$ Write down the augmented matrix for the given linear system of equations: -4x-9y=-49 and 1x-8y=-80 Find the value of the variables using Cramer’s rule: 6x+2y=-58  and -5x+9y=-101. Convert the given matrix equation into the linear system of equations. $\begin{bmatrix} -4 & -9\\ -5 & -2 \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} =\begin{bmatrix} -47\\ -31 \end{bmatrix}$ Compute the determinant of the coefficient matrix: -9x+3y=12 and -1x+6y=75.