Find x- y and z so that A-B- where A-x-232 z 18 z y-26 z- B-y z 66 y x 2 y

Since all the corresponding elements of a matrix are equal, A=x 232z18zy+26z #160;, #160;B=yz66yx2yHere,x 2=y #160; #160; #160; #160; #160; #16 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Adjoint of a Matrix

Find x, y and...

Question

Find x, y and z so that A = B, where
A = $[\begin{matrix} x - 2 & 3 & 2 z \\ 18 z & y + 2 & 6 z \end{matrix}], B = [\begin{matrix} y & z & 6 \\ 6 y & x & 2 y \end{matrix}]$

Open in App

Solution

Since all the corresponding elements of a matrix are equal,

$A = [\begin{matrix} x - 2 & 3 & 2 z \\ 18 z & y + 2 & 6 z \end{matrix}], B = [\begin{matrix} y & z & 6 \\ 6 y & x & 2 y \end{matrix}] Here, x - 2 = y . . . (1) z = 3 . . . (2) 18 z = 6 y . . . (3) Putting the value of z in eq . (3), we get 18 (3) = 6 y \Rightarrow 54 = 6 y \Rightarrow y = \frac{54}{6} = 9 Putting the value of y in eq . (1), we get x - 2 = 9 \Rightarrow x = 9 + 2 \Rightarrow x = 11 ∴ x = 11, y = 9 and z = 3$

Suggest Corrections

Similar questions

Q. Find

x, y

and

z

, so that

A = B

, where

A = [\begin{matrix} x - 2 & 3 & 2 z 18 z & y + 2 & 6 z \end{matrix}], B = [\begin{matrix} y & z & 6 6 y & x & 2 y \end{matrix}]

(i) If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal then show that,

\frac{y - z}{a (b - c)} = \frac{z - x}{b (c - a)} = \frac{x - y}{c (a - b)}

(ii) If

\frac{x}{3 x - y - z} = \frac{y}{3 y - z - x} = \frac{z}{3 z - x - y}

and

x + y + z \neq 0

then show that the value of each ratio is equal to 1.

(iii) If

\frac{a x + b y}{x + y} = \frac{b x + a z}{x + z} = \frac{a y + b z}{y + z}

and

x + y + z \neq 0

then show that

\frac{a + b}{2}

.

(iv) If

\frac{y + z}{a} = \frac{z + x}{b} = \frac{x + y}{c}

then show that

\frac{x}{b + c - a} = \frac{y}{c + a - b} = \frac{z}{a + b - c}

.

(v) If

\frac{3 x - 5 y}{5 z + 3 y} = \frac{x + 5 z}{y - 5 x} = \frac{y - z}{x - z}

then show that every ratio =

\frac{x}{y}

B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)\) are in $A \times B,$ find A and B, where x,y,z are distinct elements.

Q. Let

A

and

B

be two sets such that

n (A) = 3

and

n (B) = 2

. If

(x, 1), (y, 2), (z, 1)

are in

A \times B

find

A

and

B

where

x, y

and

z

are distinct elements

Join BYJU'S Learning Program

Find x, y and z so that A = B, where A = x-232z18zy+26z, B=yz66yx2y

Since all the corresponding elements of a matrix are equal, A=x-232z18zy+26z , B=yz66yx2yHere,x-2=y ...1 z=3 ...2 18z=6y ...3Putting the value of z in eq. 3, we get183=6y⇒54=6y⇒y=546=9Putting the value of y in eq. 1, we getx-2=9⇒x=9+2⇒x=11∴ x=11, y=9 and z=3

Find x, y and z so that A = B, where
A = $[\begin{matrix} x - 2 & 3 & 2 z \\ 18 z & y + 2 & 6 z \end{matrix}], B = [\begin{matrix} y & z & 6 \\ 6 y & x & 2 y \end{matrix}]$