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Chapter 6: Problem 67

What are equal matrices?

Short Answer

Expert verified
Equal matrices are matrices of the same order and with equal corresponding entries.

Step by step solution

01

Definition of equal Matrices

Two matrices are said to be equal if and only if they have the same order (i.e., the same number of rows and columns), and each element of the first matrix is equal to the corresponding element of the second matrix. This can be represented as: If \(A = [a_{ij}]\) and \(B = [b_{ij}]\) are two matrices of order \(m * n\), then \(A = B\) if \(a_{ij} = b_{ij}\) for every \(i = 1, 2, ..., m\) and \(j = 1, 2, ..., n\).

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Most popular questions from this chapter

Find (if possible) the following matrices: \(a, A B\) \(\boldsymbol{b}, B A\) $$A=\left[\begin{array}{ll}4 & 2 \\\6 & 1 \\\3 & 5\end{array}\right], \quad B=\left[\begin{array}{rrr}2 & 3 & 4 \\\\-1 & -2 & 0\end{array}\right]$$

Evaluate: \(\left|\begin{array}{lllll}2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0\end{array}\right|\)

Determinants are used to show that three points lie on the same line (are collinear). If $$\left|\begin{array}{lll}x_{1} & y_{1} & 1 \\\x_{2} & y_{2} & 1 \\\x_{3} & y_{3} & 1\end{array}\right|=0$$ then the points \(\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\) and \(\left(x_{3}, y_{3}\right)\) are collinear. If the determinant does not equal 0 , then the points are not collinear. Are the points \((-4,-6),(1,0),\) and \((11,12)\) collinear?

What is meant by the order of a matrix? Give an example with your explanation.

Find (if possible) the following matrices: \(a, A B\) \(\boldsymbol{b}, B A\) $$A=\left[\begin{array}{l}-1 \\\\-2 \\\\-3\end{array}\right], \quad B=\left[\begin{array}{lll} 1 & 2 & 3\end{array}\right]$$
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