for Sumi's shop
Grade 12 Quiz: Matrices, Vectors & Complex Numbers — Easy Version 2
Grade 12 · MathSheets Name: ____________________ Date: __________
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.
How to solve
This quiz mixes questions from different lessons, like a real test. Read each question carefully: the lesson name in front tells you what kind of problem it is. Check your answers, then practise the lessons where you made mistakes.
Example
Inverse Matrices & Cramer's Rule: Find the inverse of
| 1 | -2 | ||
| 0 | 1 |
Answer:
| 1 | 2 | ||
| 0 | 1 |
| 2 | -5 | ||
| -3 | 8 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| -5 | 1 | ||
| -4 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 1 | 2 | ||
| 3 | 1 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| -2 | 1 | ||
| -3 | 2 |
| -2 | -3 | ||
| 3 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <-3, -4> and v = <0, 1>. Find 4u + 3v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors in 3D: Dot & Cross Products
For u = <u1, u2, u3> and v = <v1, v2, v3>: the magnitude is |u| = √(u12 + u22 + u32); the dot product is the number u · v = u1v1 + u2v2 + u3v3; the cross product is the vector u × v = <u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1>. u and v are perpendicular (orthogonal) exactly when u · v = 0, and u × v is perpendicular to both u and v. A unit vector in the direction of v is v divided by |v|.
Try a similar one
Find the magnitude of v = <4, 8, -1>.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| -5 | -2 | ||
| 4 | 5 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Matrices
To add matrices, add the numbers in the same positions. For the determinant of
| a | b | ||
| c | d |
Try a similar one
Add:
| 4 | 3 | ||
| 2 | 4 |
| 3 | -2 | ||
| -5 | -2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Introduction to Vectors
The magnitude of <a, b> is √(a² + b²). To add vectors, add matching components: <a, b> + <c, d> = <a + c, b + d>. The dot product is <a, b> · <c, d> = ac + bd.
Try a similar one
Add: <-2,-3> + <2,0>
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Inverse Matrices & Cramer's Rule
For A =
| a | b | ||
| c | d |
| d | -b | ||
| -c | a |
Try a similar one
Find the inverse of
| 4 | -5 | ||
| -1 | 1 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
| 1 | 0 | ||
| -2 | -2 |
✓ Correct!
Not quite. The answer is
💡 How to solve: Matrix Multiplication
To multiply two matrices, each entry is a row of the first times a column of the second:
| a | b | ||
| c | d |
| e | f | ||
| g | h |
| ae + bg | af + bh | ||
| ce + dg | cf + dh |
Try a similar one
Multiply:
| -3 | 3 | ||
| 1 | 1 |
| -3 | 3 | ||
| 1 | -2 |
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors: Direction, Unit Vectors & Angles
The angle between u and v satisfies cos θ = u · v|u||v|. A vector with magnitude m and direction θ is <m cos θ, m sin θ>; the unit vector in the direction of v is v / |v|. Two vectors are perpendicular when u · v = 0.
Try a similar one
u = <3, 3> and v = <-1, 2>. Find 2u + v.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Vectors in 3D: Dot & Cross Products
For u = <u1, u2, u3> and v = <v1, v2, v3>: the magnitude is |u| = √(u12 + u22 + u32); the dot product is the number u · v = u1v1 + u2v2 + u3v3; the cross product is the vector u × v = <u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1>. u and v are perpendicular (orthogonal) exactly when u · v = 0, and u × v is perpendicular to both u and v. A unit vector in the direction of v is v divided by |v|.
Try a similar one
Find the magnitude of v = <2, 1, -2>.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Grade 12 Quiz: Matrices, Vectors & Complex Numbers — Easy Version 2
Answer every question. The lesson name before each question tells you which skill it checks — open that lesson if you need a reminder.