Paragraph: Let A=[ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] Question: What is A(adj A) equal to?

Correct answer: D. [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] We have : A= [ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array ] So, Determinant aligned & |A|=3(-3+4)-2(-3+4)+0=3-2=1 & A(adj A)=|A| I=1 . I=I . aligned Option (d) is correct option.

NDA 2024

Exam: NDA
Year: 2024
Subject: Mathematics
Chapter: Matrices

NDA 2024 · Mathematics · Matrices

Paragraph: Let A=[ array lll 3 & -3 & 4 2 & -3 & 4 0 & -1 & 1 array...

Paragraph: Let

A=\left[

\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}

\right]

Question: What is

A(\operatorname{adj} A)

equal to?

Options

A $\left[$ $\begin{array}{lll}5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}$ $\right]$
B $\left[$ $\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}$ $\right]$
C $\left[$ $\begin{array}{ccc}\frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{2} & 0 \\ 0 & 0 & \frac{1}{2}\end{array}$ $\right]$
D $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}$ $\right]$

Correct answer

D. $\left[$ $\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}$ $\right]$

Step-by-step solution

We have : A=

\left[

\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}

\right]$ So, Determinant

\begin{aligned} & |A|=3(-3+4)-2(-3+4)+0=3-2=1 \\ & \because \quad A(\operatorname{adj} A)=|A| I=1 . I=I . \end{aligned}$

Option (d) is correct option.

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