Math  /  Algebra

QuestionGiven A=[4xz6]A=\left[\begin{array}{cc}4 & x \\ z & -6\end{array}\right] and B=[y3106]B=\left[\begin{array}{cc}y & 3 \\ 10 & -6\end{array}\right], is it possible that A=BA=B ? If it is possible, for what values of x,yx, y, and zz will A=BA=B ? If it is not possible, explain why.
Part: 0/20 / 2
Part 1 of 2 It is possible that A=BA=B. It is not possible that A=BA=B.

Studdy Solution

STEP 1

1. Matrices A A and B B are equal if and only if all corresponding elements are equal.
2. We will compare each element of matrix A A with the corresponding element of matrix B B .

STEP 2

1. Compare corresponding elements of matrices A A and B B .
2. Determine if it is possible for A=B A = B and find the values of x,y, x, y, and z z if possible.

STEP 3

Compare the elements in the first row, first column of both matrices:
4=y 4 = y

STEP 4

Compare the elements in the first row, second column of both matrices:
x=3 x = 3

STEP 5

Compare the elements in the second row, first column of both matrices:
z=10 z = 10

STEP 6

Compare the elements in the second row, second column of both matrices:
6=6 -6 = -6

STEP 7

Since all corresponding elements can be made equal, it is possible for A=B A = B . The values of x,y, x, y, and z z are:
y=4,x=3,z=10 y = 4, \quad x = 3, \quad z = 10
The solution is that it is possible for A=B A = B with the values y=4 y = 4 , x=3 x = 3 , and z=10 z = 10 .

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