Find the determinant of matrix B.

Question

ScanSolve AI Tutor · Accepted Answer

Ili kupata determinant ya matrix B, tutatumia njia ya upanuzi wa cofactor. Matrix iliyotolewa ni: B = 1 & 2 & 3 3 & 2 & 1 2 & 0 & 2 Step 1: Tumia fomula ya determinant kwa matrix ya 3 × 3. Fomula ya determinant ya matrix a & b & c d & e & f g & h & i ni a(ei − fh) − b(di − fg) + c(dh − eg). Step 2: Badilisha namba kutoka matrix B kwenye fomula. |B| = 1 · det 2 & 1 0 & 2 − 2 · det 3 & 1 2 & 2 + 3 · det 3 & 2 2 & 0 Step 3: Kokotoa determinants za matrix ndogo za 2 × 2. det 2 & 1 0 & 2 = (2 × 2) − (1 × 0) = 4 − 0 = 4 det 3 & 1 2 & 2 = (3 × 2) − (1 × 2) = 6 − 2 = 4 det 3 & 2 2 & 0 = (3 × 0) − (2 × 2) = 0 − 4 = −4 Step 4: Badilisha matokeo haya kwenye fomula kuu na kurahisisha. |B| = 1 · (4) − 2 · (4) + 3 · (−4); |B| = 4 − 8 − 12; |B| = −4 − 12; |B| = −16 Determinant ya matrix B ni: −16

Find the determinant of matrix B.

Answer

Step-by-step solution

Tumia fomula ya determinant kwa matrix ya $3 \times 3$ .

Badilisha namba kutoka matrix $B$ kwenye fomula.

Kokotoa determinants za matrix ndogo za $2 \times 2$ .

Badilisha matokeo haya kwenye fomula kuu na kurahisisha.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Find the determinant of matrix B.

Answer

Step-by-step solution

Tumia fomula ya determinant kwa matrix ya 3×33 \times 33×3.

Badilisha namba kutoka matrix BBB kwenye fomula.

Kokotoa determinants za matrix ndogo za 2×22 \times 22×2.

Badilisha matokeo haya kwenye fomula kuu na kurahisisha.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Tumia fomula ya determinant kwa matrix ya $3 \times 3$ .

Badilisha namba kutoka matrix $B$ kwenye fomula.

Kokotoa determinants za matrix ndogo za $2 \times 2$ .