Redwood High School. Department of Mathematics
Hard worker's name:___________________________________
2015-2016 Geometry worksheet for Test S2 #7 Matrices v6.
Solve the system, using Matrices.
1) 4x + 9y - z = 26
x - 5y - 7z = -62
-4x + y + z = -6
2)
1)
2)
5x - y+ 2z = 38
5x
+ 5z = 60
7y + z = 14
3) -4x - y + 2z = -13
-9x + 5y + 4z = 32
-3x - 8y + z = -79
3)
4) x - 2y + 3z = 11
4x + y - z = 4
2x - y + 3z = 10
4)
5) 2x + 8y + 6z = 20
4x + 2y - 2z = -2
3x - y + z = 11
5)
Evaluate the determinant.
6) 5 2
-2 5
6)
Find A-1 if it exists. By hand
7) A = 2 -5
1 2
7)
Find the inverse of the matrix. (by hand)
8) A = -2 -2
0 1
Solve the system by Matrices.
9) 8x + 9y = 81
2x - 4y = -36
9)
Solve the system of equations using Matrices.
3
10) 2x + y - z = 5
2
10)
1
x - 3z = 16
2
x - 5y = -24
1
11) -0.2x + 0.3y + 0.1z = -0.1
-0.6x + 0.4y + 0.2z = -1.2
0.4x - 0.4y + 0.2z = 0.2
Solve the problem.
12)
Let A = 1 3
25
13)
16)
12)
and B = 0 4 . Find 2A + B.
-1 6
-3 -4 1
Let A = -9 -1 -3
-7 -1 6
-7 7 -6
and B = -8 4 -4 . Find -2A - 4B.
-1 -9 -1
Solve the matrix equation for X.
14)
2 -2
5 0
Let A = -4 0 and B = 0 -5 ;
5 8
2 8
15)
11)
1 -4
Let A = 0 -2
9 -7
9 -9
and B = -1 -4 ;
0 8
4 1 -2
Let A = 5 0 0
1 -4 2
13)
14)
4X + A = B
15)
B - X = 3A
16)
-1 -4 -2
and B = 0 1 1 ;
5 0 4
2B - 2A = X
Solve the system using matrices.
17) -3x + 4y - z = 23
x + 6y - 8z = 26
5x + y + z = 21
17)
18) -3x - y + 5z = 6
-4x - 4z = -16
7y + z = 45
18)
19) x + y + z = -1
x - y + 5z = -15
3x + 3y + 3z = 7
19)
20) 4x + y = -22
-2y + 4z = 12
4x + 3y - 4z = -34
20)
2
Answer Key
Testname: GEOMETRY S2 TEST 7 MATRICES WKSV6
1)
2)
3)
4)
5)
6)
7)
{(4, 2, 8)}
{(5, 1, 7)}
{(5, 9, 8)}
{(2, -3, 1)}
{(2, -1, 4)}
29
2
9
5
9
-
1
9
2
9
-
1
-1
2
8)
0 1
9) {(0, 9)}
10) (-4, 4, -6)
11) (3, 2, -1)
12)
2 10
3 16
13)
34 -20 22
50 -14 22
18 38 -8
14)
3
1
4
2
X=
-
15)
X=
16)
1 -
5
4
3
4
0
6 3
-1 2
-27 29
-10 -10 0
X = -10
2 2
8
8 4
17) (2, 8, 3)
18) (1, 6, 3)
19) inconsistent system
20) dependent system
3