This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) To find the values of x, y, and z, we equate the corresponding elements of the given matrices: x+y & z-x \\ y+2z & x = 3 & 2 \\ 8 & 1 This gives us the following system of equations: 1. x+y = 3 2. z-x = 2 3. y+2z = 8 4. x = 1 Step 1: From equation (4), we directly get the value of x. x = 1 Step 2: Substitute x=1 into equation (1). 1+y = 3 y = 3-1 y = 2 Step 3: Substitute x=1 into equation (2). z-1 = 2 z = 2+1 z = 3 Step 4: Verify these values with equation (3). y+2z = 2+2(3) = 2+6 = 8 The values satisfy all equations. The values are: x=1, y=2, z=3 b) To find the values of x, y, p, and q, we equate the corresponding elements of the given matrices: p+1 & 5 \\ -3 & q = 6 & y-3 \\ x & -2 This gives us the following system of equations: 1. p+1 = 6 2. 5 = y-3 3. -3 = x 4. q = -2 Step 1: Solve for p from equation (1). p+1 = 6 p = 6-1 p = 5 Step 2: Solve for y from equation (2). 5 = y-3 y = 5+3 y = 8 Step 3: From equation (3), we directly get the value of x. x = -3 Step 4: From equation (4), we directly get the value of q. q = -2 The values are: x=-3, y=8, p=5, q=-2