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Chapter 6: Problem 70

Describe how to subtract matrices.

Short Answer

Expert verified
To subtract two matrices, they must have the same dimensions. Then, perform the subtraction cell by cell, resulting in a new matrix with each cell being the difference between the corresponding cells in the original matrices.

Step by step solution

01

Securing matching dimensions

First of all, you want to make sure that the two matrices to be subtracted from each other have the same dimensions, i.e., the same number of rows and columns. If they don't, the subtraction cannot be performed.
02

Performing the subtraction

When matrices have the same size, subtraction can be done element by element. This meaning, for each cell in the first matrix, subtract the corresponding cell in the second matrix. This corresponds to (element of the first matrix) - (corresponding element of the second matrix).
03

Result Matrix

After performing the subtraction for all cells, the result will be a new matrix of the same size. Each cell of this resulting matrix is the result of the subtraction between the corresponding cells in the first and second matrices.

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Most popular questions from this chapter

The figure shows the letter \(L\) in a rectangular coordinate system. (GRAPH CANNOT COPY) The figure can be represented by the matrix $$B=\left[\begin{array}{llllll}0 & 3 & 3 & 1 & 1 & 0 \\\0 & 0 & 1 & 1 & 5 & 5\end{array}\right]$$ Each column in the matrix describes a point on the letter. The order of the columns shows the direction in which a pencil must move to draw the letter. The \(L\) is completed by connecting the last point in the matrix, \((0,5),\) to the starting point, \((0,0) .\) Use these ideas to solve Exercises \(53-60 .\) a. If \(A=\left[\begin{array}{rr}-1 & 0 \\ 0 & 1\end{array}\right],\) find \(A B\) b. Graph the object represented by matrix \(A B\). What effect does the matrix multiplication have on the letter \(L\) represented by matrix \(B ?\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can speed up the tedious computations required by Cramer's Rule by using the value of \(D\) to determine the value of \(D_{x^{*}}\)

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

Find \(A^{-1}\) and check. $$A=\left[\begin{array}{cc}e^{2 x} & -e^{x} \\\e^{3 x} & e^{2 x}\end{array}\right]$$

Explain how to find the multiplicative inverse for a \(3 \times 3\) invertible matrix.
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