NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.1 Question 6

Question

Find x,y,z in (i) $\left[\begin{matrix}4 & 3\x & 5\end{matrix}\right]$ = $\left[\begin{matrix}y & z\1 & 5\end{matrix}\right]$; (ii) $\left[\begin{matrix}x + y & 2\z + 5 & x y\end{matrix}\right]$ = $\left[\begin{matrix}6 & 2\5 & 8\end{matrix}\right]$; (iii) $\left[\begin{matrix}x + y + z\x + z\y + z\end{matrix}\right]$ = $\left[\begin{matrix}9\5\7\end{matrix}\right]$.

Accepted Answer

Final Answer: (i) x=1,y=4,z=3; (ii) (x,y,z)=(2,4,0) or (4,2,0); (iii) (2,4,3). Step 1: Equate corresponding entries; no matrix entry can be ignored. Step 2: (i) The entries give y=4,z=3,x=1. Step 3: (ii) x+y=6,xy=8,z=0. Thus x,y are the roots of u²−6u+8=(u−2)(u−4)=0, in either order. Step 4: (iii) From total 9, subtract y+z=7 to get x=2; subtract x+z=5 to get y=4; then z=3.

NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.1 Question 6

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