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Chapter 9: Problem 70

Describe matrices that cannot be added or subtracted.

Short Answer

Expert verified
Matrices that do not have the same order, meaning the same number of rows and columns, cannot be added or subtracted.

Step by step solution

01

Understanding Addition and Subtraction of Matrices

Addition and subtraction of matrices require that the two matrices have the same dimension. This means that matrices must be of the same order, i.e., they must have the same number of rows and the same number of columns.
02

Describing Matrices Which Cannot Be Added or Subtracted

If any matrix does not fulfill the requirement mentioned above, they cannot be added or subtracted. Concretely, two matrices A and B cannot be added or subtracted if the rows of A are not equal to the rows of B or columns of A are not equal to the columns of B. Hence, the matrices that can't be added or subtracted are those with dissimilar orders.

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Most popular questions from this chapter

Let $$ \begin{aligned} A &=\left[\begin{array}{cc} {1} & {0} \\ {0} & {1} \end{array}\right], \quad B=\left[\begin{array}{rr} {1} & {0} \\ {0} & {-1} \end{array}\right], \quad C=\left[\begin{array}{rr} {-1} & {0} \\ {0} & {1} \end{array}\right] \\ D &=\left[\begin{array}{rr} {-1} & {0} \\ {0} & {-1} \end{array}\right] \end{aligned} $$ Use any three of the matrices to verify an associative property.

Exercises \(72-74\) will help you prepare for the material covered in the next section. In each exercise, refer to the following system: $$ \left\\{\begin{aligned} 3 x-4 y+4 z &=7 \\ x-y-2 z &=2 \\ 2 x-3 y+6 z &=5 \end{aligned}\right. $$ Show that \((12 z+1,10 z-1, z)\) satisfies the system for \(z=0\)

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

Solve each system of equations using matrices. Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \left\\{\begin{array}{r} {3 a-b-4 c=3} \\ {2 a-b+2 c=-8} \\ {a+2 b-3 c=9} \end{array}\right. $$

Perform the indicated matrix operations given that \(A, B,\) and \(C\) are defined as follows. If an operation is not defined, state the reason. $$ A=\left[\begin{array}{rr} {4} & {0} \\ {-3} & {5} \\ {0} & {1} \end{array}\right] \quad B=\left[\begin{array}{rr} {5} & {1} \\ {-2} & {-2} \end{array}\right] \quad C=\left[\begin{array}{rr} {1} & {-1} \\ {-1} & {1} \end{array}\right] $$ $$ A(B+C) $$
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