If A=[ array cc 4 i-6 & 10 i 14 i & 6+4 i array ] and k= 1 2 i^ where i= -1 , then kA is equal to

Correct answer: A. [ array cc 2+3 i & 5 7 & 2-3 i array ] A=[ array cc 4 i-6 & 10 i 14 i & 6+4 i array ] and K=(1)/(2 i)K= 1 2 i = i 2 i(i) = i 2 i^2 = -i 2 . KA= -i 2 [ array cc 4 i-6 & 10 i 14 i & 6+4 i array ]=[ array cc (4 i-6)((-i)/(2)) & 10 i((-i)/(2)) 14 i((-i)/(2)) & (6+4 i)((-i)/(2)) array ]= [ array cc -2 i^2+3 i & -5 i^2 -7 i^2 & -3 i-2 i^2 array ]=[ array cc 2+3 i & 5 7 & 2-3 i array ]

NDA 2017

Exam: NDA
Year: 2017
Subject: Mathematics
Chapter: Matrices

NDA 2017 · Mathematics · Matrices

If A=[ array cc 4 i-6 & 10 i 14 i & 6+4 i array ] and k= 1 2 i^...

A=\left[

\begin{array}{cc}4 i-6 & 10 i \\ 14 i & 6+4 i\end{array}

\right] and

k=\frac{1}{2 i^{\prime}}

where

i=\sqrt{-1}$, then kA is equal to

Options

A $\left[$ $\begin{array}{cc}2+3 i & 5 \\ 7 & 2-3 i\end{array}$ $\right]$
B $\left[$ $\begin{array}{cc}2-3 \mathrm{i} & 5 \\ 7 & 2+3 \mathrm{i}\end{array}$ $\right]$
C $\left[$ $\begin{array}{cc}2-3 i & 7 \\ 5 & 2+3 i\end{array}$ $\right]$
D $\left[$ $\begin{array}{cc}2+3 \mathrm{i} & 5 \\ 7 & 2+3 \mathrm{i}\end{array}$ $\right]$

Correct answer

A. $\left[$ $\begin{array}{cc}2+3 i & 5 \\ 7 & 2-3 i\end{array}$ $\right]$

Step-by-step solution

A=\left[

\begin{array}{cc}4 i-6 & 10 i \\ 14 i & 6+4 i\end{array}

\right]

and

K=\frac{1}{2 i}\mathrm{K}=\frac{1}{2 \mathrm{i}}=\frac{\mathrm{i}}{2 \mathrm{i}(\mathrm{i})}=\frac{\mathrm{i}}{2 \mathrm{i}^2}=\frac{-\mathrm{i}}{2}

.

\therefore \mathrm{KA}=\frac{-\mathrm{i}}{2}\left[

\begin{array}{cc}4 \mathrm{i}-6 & 10 \mathrm{i} \\ 14 \mathrm{i} & 6+4 \mathrm{i}\end{array}

\right]=\left[

\begin{array}{cc}(4 i-6)\left(\frac{-i}{2}\right) & 10 i\left(\frac{-i}{2}\right) \\ 14 i\left(\frac{-i}{2}\right) & (6+4 i)\left(\frac{-i}{2}\right)\end{array}

\right]=

\left[

\begin{array}{cc}-2 \mathrm{i}^2+3 \mathrm{i} & -5 \mathrm{i}^2 \\ -7 \mathrm{i}^2 & -3 \mathrm{i}-2 \mathrm{i}^2\end{array}

\right]=\left[

\begin{array}{cc}2+3 \mathrm{i} & 5 \\ 7 & 2-3 \mathrm{i}\end{array}

\right]

Practice Matrices on Quantrex Academy →

More from Matrices

Consider the following statements : I. If n× n(n > 1) matrix is symmetric, then its… NDA 2026 If M is a square matrix such that M^3=M , then how many values of |M| are possible ? NDA 2026 If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is… NDA 2026 If M^ T is the transpose of a 2×2 matrix M , then which of the following is/are correct ?… NDA 2026 Consider the following in respect of non-singular matrices A and B : I. (AB)^ -1 = A^ -1… NDA 2025 For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is [adj\… NDA 2025 Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29… NDA 2025 If [x \ 1 \ 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45]… NDA 2025 If A = pmatrix 1 & 2 & 2 2 & 1 & 2 2 & 2 & 1 pmatrix , then what is A^2 - 4A equal to? NDA 2025 If A = pmatrix y & z & x z & x & y x & y & z pmatrix where x , y , z are integers, is an… NDA 2025 If A = pmatrix x & y & z y & z & x z & x & y pmatrix where x , y , z are integers, is an… NDA 2025 For the following two (02) items: Let A = pmatrix θ & θ - θ & θ pmatrix . What is the… NDA 2025 What is the value of the determinant of the inverse of the matrix pmatrix -4 & -5 2 & 2… NDA 2025 If f(θ) = pmatrix θ & θ - θ & θ pmatrix , then what is \ f(π)\ ^2 equal to? NDA 2025 Let X be a matrix of order 3 × 3, Y be a matrix of order 2 × 3 and Z be a matrix of order… NDA 2024 Let A and B be two square matrices of same order. If A B is a null matrix, then which one… NDA 2024 Full Matrices list Matrices JEE Maths PYQs JEE Mathematics PYQs All NDA PYQs