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Chapter 4: Q1. (page 198)

Write the $4 \times 4$ identity matrix.

Short Answer

Expert verified

The $4 \times 4$ identity matrix is: $[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$

Step by step solution

01

- Description of step.

An identity matrix is a matrix which has entries in all diagonal elements as 1 and 0 in the non-diagonal elements.

02

- Description of step.

As, a $4 \times 4$ identity matrix is to be constructed that implies a matrix having four rows and 4 columns and having all diagonal elements as 1 and non-diagonal elements as 0 .

03

- Write the 4×4 identity matrix.

The $4 \times 4$ identity matrix is: $[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix}]$

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Most popular questions from this chapter

Perform the indicated matrix operation. If the matrix doesn’t exist, write impossible.

14. $[\begin{matrix} 4 \\ 1 \\ - 2 \end{matrix}] + [\begin{matrix} 6 \\ - 5 \\ 8 \end{matrix}]$

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Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

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Use matrices $A$ , $B$ , $C$ and $D$ to find the following.

$A = [\begin{matrix} 5 & 7 \\ - 1 & 6 \\ 3 & - 9 \end{matrix}], B = [\begin{matrix} 8 & 3 \\ 5 & 1 \\ 4 & 4 \end{matrix}], C = [\begin{matrix} 0 & 4 \\ - 2 & 5 \\ 7 & - 1 \end{matrix}], D = [\begin{matrix} 6 & 2 \\ 9 & 0 \\ - 3 & 0 \end{matrix}]$

28. $3 C - 4 A + B$

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