Chapter 4: Q3. (page 163)

Write a matrix that, when added to a $3 \times 2$ matrix, increases each element in the matrix by 4.

Short Answer

Expert verified

A matrixwhen added to a $3 \times 2$ matrix, increases each element in the matrix by 4 is $A = [\begin{matrix} 4 & 4 \\ 4 & 4 \\ 4 & 4 \end{matrix}]$ .

Step by step solution

- Define concept of matrix addition

If A and B are two matrices of order $m \times n$ , then the addition of the two matrices will also yield a matrix of order $m \times n$ wherein each element is the sum of the corresponding elements.

- Write the required matrix

In order to find a matrix that when added to a $3 \times 2$ matrix, increases each element in the matrix by 4 note that since matrices are to be added therefore the order of both the matrices must be same. Consider a matrix of order $3 \times 2$ , $A = [\begin{matrix} 4 & 4 \\ 4 & 4 \\ 4 & 4 \end{matrix}] .$

- Verify

Add the matrices A to a matrix $B = [\begin{matrix} 1 & 0 \\ 2 & 3 \\ 5 & - 1 \end{matrix}]$ chosen at random. So as to verify if $A$ when added to B increases each element in the matrix by 4, add the corresponding elements of both the matrices.

$\begin{matrix} A + B = [\begin{matrix} 4 & 4 \\ 4 & 4 \\ 4 & 4 \end{matrix}] + [\begin{matrix} 1 & 0 \\ 2 & 3 \\ 5 & - 1 \end{matrix}] \\ = [\begin{matrix} 4 + 1 & 4 + 0 \\ 4 + 2 & 4 + 3 \\ 4 + 5 & 4 + (- 1) \end{matrix}] \\ = [\begin{matrix} 5 & 4 \\ 6 & 7 \\ 9 & 3 \end{matrix}] \end{matrix}$

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Write a matrix that, when added to a $3 \times 2$ matrix, increases each element in the matrix by 4.

Short Answer

Step by step solution

- Define concept of matrix addition

- Write the required matrix

- Verify

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Write a matrix that, when added to a 3×2matrix, increases each element in the matrix by 4.

Short Answer

Step by step solution

- Define concept of matrix addition

- Write the required matrix

- Verify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Geometry

Applied Mathematics

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write a matrix that, when added to a $3 \times 2$ matrix, increases each element in the matrix by 4.