Math Problem Statement

Perhatikan matriks berikut: A = [1 4 -7; 2 0 5]. Which statement is true? A. Matrices A is 3x4 B. Matrix A is rectangular C. Determinant of matrix A = 0 D. Matrix A is square E. Matrix A is upper triangular

Solution

This image contains a set of matrix-related math problems. Let's go through one of them.

The first question is:

1. Perhatikan matriks berikut:

A=(147205)A = \begin{pmatrix} 1 & 4 & -7 \\ 2 & 0 & 5 \end{pmatrix}

Which of the following statements is true?

A. Matrices AA is 3×43 \times 4

B. Matrix AA is a rectangular matrix

C. Determinant of matrix A=0A = 0

D. Matrix AA is a square matrix

E. Matrix AA is an upper triangular matrix

Solution:

  1. Matrix AA has dimensions 2×32 \times 3 because it has 2 rows and 3 columns. This eliminates options A and D because matrix A is not square.

  2. Matrix AA is a rectangular matrix, meaning it has more columns than rows, which makes option B correct.

  3. The determinant is not defined for a non-square matrix, eliminating option C.

  4. Matrix A cannot be upper triangular since it is not square, eliminating option E.

Conclusion:

The correct answer is B. Matrix A is a rectangular matrix.

Would you like me to explain more details or solve another problem from this sheet? Here are five questions related to this topic:

  1. What is the difference between square and rectangular matrices?
  2. How can we calculate the determinant of a square matrix?
  3. What are upper triangular and lower triangular matrices?
  4. Can a rectangular matrix be used in matrix multiplication?
  5. What conditions must be met for a matrix to be invertible?

Tip: For non-square matrices, operations like finding determinants and inverses are not defined!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Matrices
Matrix Dimensions
Matrix Types

Formulas

Matrix dimensions: m x n
Determinant of a matrix
Upper triangular matrix

Theorems

Properties of rectangular matrices

Suitable Grade Level

Grades 10-12