Matrix - practice problems
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, typically enclosed in brackets. Matrices are denoted by capital letters with dimensions m×n (m rows, n columns). Operations include addition (same dimensions), scalar multiplication, matrix multiplication (where the number of columns in the first equals rows in the second), and finding determinants and inverses for square matrices. Matrices represent linear transformations, systems of linear equations, and data structures in various applications. Special matrices include identity matrices (diagonal of ones), zero matrices, diagonal matrices, and symmetric matrices. Applications span computer graphics, economics, physics, engineering, statistics, and machine learning where matrices efficiently represent and manipulate multi-dimensional data.Instructions: For each problem, solve carefully and show your complete working.
Number of problems found: 41
- Matrices 2
Suppose A=(1 6 3 −2) B=(4 −3 −4 3) find 2A+3B - Matrix column count
Matrix E is a rectangular matrix that contains 48 elements and four rows. How many columns does this matrix have? - Inverse matrix columns
Find how many columns will contain the inverse matrix to matrix C if matrix C contains nine elements. - The inverse
The inverse matrix for matrix A has a determinant value of 0.333. What value is a determinant of matrix A? - The sum 17
The sum of the three numbers is -1. If we multiply the second number by 2, the third number by 3, and add them, we get 5. If we subtract the third number from the sum of the first and second numbers, we get -1. Answer the following: Represent the above - Matrix Square Determinant
The determinant of matrix J has the value 0. What will be the value of the determinant of matrix C, which we get as the square of matrix J? - Matrix Row Operation Rank The rank of matrix A is 3. What rank will this matrix have if we add twice the second row to its first row?
- Matrix determinant change
We have a matrix of order n ≥ 3. If we add the last column to each column (including the last), how does its determinant change? - Matrix Sarruss Rule Rows How many rows does a square matrix A have if we use Sarruss's rule to calculate its determinant?
- Matrix determinant value The determinant of matrix C is equal to 12. What will the value of the determinant of matrix F be if we know that matrix F is the opposite matrix of matrix C?
- Determinant Product Matrices The determinant of the product of 2 square matrices has the value 3. What is the product's value of the respective determinants of these matrices?
- Matrix determinant
The inverse matrix determinant to matrix C has a value of 0.125. Determine how often the determinant of the matrix C is larger than the determinant of the inverse matrix to the matrix C. - Matrix determinant The determinant of the inverse matrix to matrix B has a value of 0.25. What is the value of the determinant of matrix B?
- Singular Matrix Rank What is the rank of a second-order square matrix if we can only say that it is singular?
- Matrix columns
The rectangular matrix contains 12 elements and three rows. How many columns does this matrix have? - Regular Matrix Rank What is the rank of a second-order square matrix if we can say that this matrix is regular?
- Determinant of Zero Matrix Determine the determinant of a square matrix of type 4x4 if we know that it is zero.
- Number of Matrix Elements The rectangular matrix contains three rows and four columns. Determine how many elements this matrix contains.
- Determinant of Inverse Matrix What number do we get if we multiply the determinant of matrix A by the determinant of its inverse matrix?
- Square Matrix Order Elements How many orders are a square matrix C if this matrix contains 36 elements?
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